chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
4,774 | lean_file_chunk | 37afa09015a824cf69d1b796c940d6c8e58ccb9764f7f79865821b744b11e7f8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mihai Iancu, Stefan Kebekus, Sebastian Schleissinger, Aristotle AI
-/
module
public import Mathlib.Analysis.Complex.Harmonic.MeanValue
public import Mathlib.Analysis.Complex.Poisson
... |
9,215 | lean_file_chunk | 82827bbca08c24054951d414c17c4d933018b603636a7e25a598f48846f7f014 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.Complex.Circle
public import Mathlib.Analysis.Normed.Module.Ball.Action
public import Mathlib.Algebra.Group.PNatPowAssoc
/-!... |
7,401 | lean_file_chunk | 027474715f53fd3501f6925ff4d4fe1429814e81d091b57e9434d53f8c8b0e24 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
module
public import Mathlib.Analysis.Complex.JensenFormula
public import Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction
/-!
# The First Main The... |
10,064 | lean_file_chunk | 5e5ae7d933b62fda11fb79958b32f92aa5eba19c5fdb2d18b3ac8bc15813062d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
module
public import Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic
public import Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic
/-!
# The... |
1,780 | lean_file_chunk | c1cddfd5b5cdf5187eda8be349bf32eea9eb6c3d590493cd5f5b755da346b57b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
public import Mathlib.Analysis.Complex.Periodic
public import Mathlib.Analysis.Complex.Upp... |
15,998 | lean_file_chunk | 04725002ab29c9f08b1e653f6ce06c1d19c54827bc4f40e1acb8903524569a0e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.Complex.UpperHalfPlane.Topology
public import Mathlib.Analysis.SpecialFunctions.Arsinh
public import Mathlib.Geometry.Euclide... |
8,489 | lean_file_chunk | d8bb3fe37cd0a3abd3cf6c046302b9ddf9684ff54cd1e39d73b4c606b1b6aa45 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction
public import Mathlib.Analysis.Convex.Contractible
public import Mathlib.Analysis.Locall... |
5,775 | lean_file_chunk | e7d8a0f597455d99617543876182586aa2be4294e19b8f856dedb50467b31541 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Complex.UpperHalfPlane.Topology
public import Mathlib.Analysis.Matrix.Normed
public import Mathlib.Topology.Algebra.Group.Matri... |
7,808 | lean_file_chunk | 64bdef209593ee8d2c3d95e478fdbdc583e9bd6b428b1b2072aca6f751666f06 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
-/
module
public import Mathlib.Analysis.Complex.Basic
/-!
# The upper half plane
This file defi... |
3,860 | lean_file_chunk | e88dbd49872ea7aeff5de0f74176647e60dc690ec4dc4ff258393515484b2902 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler
-/
module
public import Mathlib.Algebra.Module.Submodule.Basic
public import Mathlib.Analysis.Complex.UpperHalfPlane.Topology
public import Mathlib.Orde... |
4,694 | lean_file_chunk | 414d97cd1ef0241785ece47b947427a73a6f2cedfa463fcdfc06beb35ae68154 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.RestrictScalars
public import Mathlib.Analysis.Complex.UpperHalfPlane.Topology
public import Mathlib.Analysis.... |
16,495 | lean_file_chunk | 1f1a82ca0849f19c6af9f0ed7652f064a203131247ad87027d50e03ff54473b1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
-/
module
public import Mathlib.Analysis.Complex.UpperHalfPlane.Basic
public import Mathlib.Linear... |
10,907 | lean_file_chunk | 19b56955d0ac7922a102badce26c0c137dcc8225a4df559e1062d86c6fed1219 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler
-/
module
public import Mathlib.Analysis.Complex.CauchyIntegral
public import Mathlib.Analysis.Complex.UpperHalfPlane.Topology
public import Mathlib.Ana... |
4,332 | lean_file_chunk | f629d9b9001cc2873f00f493dff5afb488e9098e2c2ca1aecd1dbc8f17e7c09e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Aristotle AI
-/
module
public import Mathlib.Analysis.Complex.Polynomial.Basic
/-!
# Gauss-Lucas Theorem
In this file we prove Gauss-Lucas Theorem:
the roots of th... |
9,005 | lean_file_chunk | c01662e59949bf2787cc41710c3ee8a882f0526035115f6011a7daa87a030a2b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Calculus.Deriv.Polynomial
public import Mathlib.Analysis.Complex.Liouville
public import Mathlib.FieldT... |
1,475 | lean_file_chunk | c221d509b71b7000a1714bc823a6a31658fdd3827b882dd5d0f45599b2367edf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Algebra.Polynomial.UnitTrinomial
public import Mathlib.Analysis.Complex.Polynomial.Basic
/-!
# Irreducibility of unit trinomials
## ... |
9,698 | lean_file_chunk | 48511d04ec3a6abf7a392863f02ddf165434943d4c760120a64265cee3247434 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
module
public import Mathlib.Algebra.Order.WithTop.Untop0
public import Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic
public import Mathlib.MeasureT... |
5,137 | lean_file_chunk | 4f0d49c027f4f6f372d501ed4bd28d135adc286650075f21bb7dc6aa5b07e21e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
module
public import Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic
/-!
# Asymptotic Behavior of the Logarithmic Counting Function
If `f` is meromorp... |
23,974 | lean_file_chunk | 2ca499529236d04d429826cb76aa8d5b96eeb8db353700cfbc67c9876ec3e413 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
module
public import Mathlib.Analysis.Complex.JensenFormula
/-!
# The Logarithmic Counting Function of Value Distribution Theory
For nontrivially normed fields `𝕜... |
998 | lean_file_chunk | 9625c273a4919e5f26468862503f1a1b898e55bd4be6cfd98ce0578012a2c979 | lean_source_file | pkg_mathlib_source_file_chunks | logCounting (divisor f ⊤) R =
circleAverage (log ‖f ·‖) 0 R - log ‖meromorphicTrailingCoeffAt f 0‖ := by
have h₁f : MeromorphicOn f (closedBall 0 |R|) := by tauto
simp only [MeromorphicOn.circleAverage_log_norm hR h₁f, logCounting, top_eq_univ,
AddMonoidHom.coe_mk, ZeroHom.coe_mk, zero_sub, norm_neg, add_... |
2,882 | lean_file_chunk | d8881d7f8f331d9b3f1a7f25ea87c167273695b755f993eafde49fa287c4bef5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.BigOperators.Expect
public import Mathlib.Algebra.Group.AddChar
public import Mathlib.Analysis.RCLike.In... |
8,775 | lean_file_chunk | 315838f7e1ca0721b66580227bac552491f9f96af49b35413e80ebde2d3a728f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.DirectSum.AddChar
public import Mathlib.Analysis.Fourier.FiniteAbelian.Orthogonality
public import Mathl... |
4,408 | lean_file_chunk | a0504440b9a9652dc0e017d0f469365d0afe108fb431747d2535ee3028935d36 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Hanting Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hanting Zhang
-/
module
public import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
/-! # The Wallis formula for Pi
This file establishes the Wallis product for `π` (`Real.tendst... |
13,594 | lean_file_chunk | 8fa707995011ab83c6dca539f467dc0cb9e3c9b1610fce9656ace0775509565d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
public import Mathlib.Topology.Algebra.Order.Floor
public import Mathlib.NumberTheory.Real.Irratio... |
2,278 | lean_file_chunk | d52b89f2a7afad63e04c37a6f5acece4a89b0edd4a25ec734f6100f066ffa992 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
meta import Batteries.Data.Rat.Float -- shake: keep (for `#eval` sanity check)
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan
public import... |
2,686 | lean_file_chunk | db4cd746013d066836bbc04fb64d15ce68a658882c79ed79c4276e0e1006341d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson, Jeremy Tan
-/
module
public import Mathlib.Analysis.Complex.AbelLimit
public import Mathlib.Analysis.SpecialFunctions.Complex.Arctan
/-! ### Leibniz's series fo... |
11,515 | lean_file_chunk | e3734afd745fd3ecc3f5f0cffa3e60da8a31177ebdf2510c7eddea81534774f7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Mario Carneiro
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds
/-!
# Pi
This file contains lemmas which establish bounds on `Real.... |
9,212 | lean_file_chunk | 426dcb4add74e600f3f88c0255f6f64aed5dd690790484f19d70b783f45cfbc8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen
-/
module
public import Mathlib.Topology.MetricSpace.Cover
/-!
# Delone sets
A **Delone set** `D ⊆ X` in a metric space is a set which is both:
* **Uniformly Discrete*... |
14,936 | lean_file_chunk | c909009cfcf24effe69d43c7eeadb8f85c2f3a82bf4bb30b8e4150c6032313c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Moritz Doll
-/
module
public import Mathlib.Analysis.Distribution.SchwartzSpace.Deriv
public import Mathlib.Analysis.Fourier.FourierTransformDeriv
public import ... |
15,032 | lean_file_chunk | 8f4891ad868a0e4f3219f99bcd38eb32627d02f4a124e201734e1d439b65c9b8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
module
public import Mathlib.Analysis.Distribution.SchwartzSpace.Basic
public import Mathlib.Analysis.Calculus.IteratedDeriv.Defs
public import Mathlib.Analysis.Calculus.L... |
23,956 | lean_file_chunk | 0ab922f3dc094e33a36b156e7be695fd45191033395df5936a6eda4d2a79a3ec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
module
public import Mathlib.Analysis.LocallyConvex.WithSeminorms
public import Mathlib.Analysis.Normed.Group.ZeroAtInfty
public import Mathlib.Analysis.Normed.Lp.SmoothAp... |
23,997 | lean_file_chunk | 4b05390f6f2df3971e0ac34b0d9eee576b2a0673bfd63ca219d3187d015a8476 | lean_source_file | pkg_mathlib_source_file_chunks | theorem evalCLM_apply_apply (f : 𝓢(E, F →L[ℝ] G)) (m : F) (x : E) :
SchwartzMap.evalCLM 𝕜 E G m f x = f x m := rfl
end EvalCLM
section Multiplication
variable [NontriviallyNormedField 𝕜] [NormedAlgebra ℝ 𝕜]
[NormedAddCommGroup D] [NormedSpace ℝ D]
[NormedAddCommGroup G] [NormedSpace ℝ G]
[NormedSpace �... |
5,804 | lean_file_chunk | 87ba5e35a7f7c4186180ad783764fb37b2c45e5cc293d552fd8dd81ac245212d | lean_source_file | pkg_mathlib_source_file_chunks | _ ≤ eLpNorm (fun x ↦ (1 + ‖x‖) ^ (-k : ℝ)) p μ *
(2 ^ k * ENNReal.ofReal (((Finset.Iic (k, 0)).sup (schwartzSeminormFamily 𝕜 E F)) f)) := by
gcongr
refine eLpNormEssSup_le_of_ae_nnnorm_bound (ae_of_all μ fun x ↦ ?_)
rw [← norm_toNNReal, Real.toNNReal_le_iff_le_coe]
simpa [norm_smul, abs_of_nonneg... |
6,448 | lean_file_chunk | 7949c713e98f51149a374392a8477bb417235e5bb2cd861aefec3c6b1d758841 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yaël Dillies
-/
module
public import Mathlib.Analysis.Convex.Cone.Dual
public import Mathlib.Analysis.InnerProductSpace.Adjoint
/-!
# Inner dual cone of a set... |
5,843 | lean_file_chunk | 1eb0fc20ae021ced625c7811e69b2fcd56da47dbf15c5d64aa92287ea9948b7a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bjørn Solheim. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bjørn Solheim
-/
module
public import Mathlib.Analysis.Convex.Cone.Dual
public import Mathlib.Geometry.Convex.Cone.Simplicial
public import Mathlib.Geometry.Convex.Cone.TensorProduct
p... |
2,545 | lean_file_chunk | a447d2609a1166e8187553b76d14609358329bcf3f76b9e498db6e3366de4fad | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Apurva Nakade. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Apurva Nakade
-/
module
public import Mathlib.Geometry.Convex.Cone.Pointed
public import Mathlib.Topology.Algebra.ConstMulAction
public import Mathlib.Topology.Algebra.Monoid.Defs
/-!... |
9,048 | lean_file_chunk | c261b2f2d52c6b9e4e89290f1ec9b9dc04b90033a3cdfae1ebbc6e5a9fc40ddd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Frédéric Dupuis
-/
module
public import Mathlib.Data.Real.Archimedean
public import Mathlib.Geometry.Convex.Cone.Basic
public import Mathlib.LinearAlgebra.LinearPMap... |
7,997 | lean_file_chunk | 245be9231ae329035cca97b291ba4942ab2f4cab176ca4ce479933657901fa49 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Apurva Nakade. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Apurva Nakade, Yaël Dillies
-/
module
public import Mathlib.Analysis.Convex.Cone.Closure
public import Mathlib.Geometry.Convex.Cone.Pointed
public import Mathlib.Topology.Algebra.Modul... |
6,376 | lean_file_chunk | 7f58c785eb2f855db4fa13b3ffb2694db3df5a009fdc92468716641ee1c0f468 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Andrew Yang
-/
module
public import Mathlib.Analysis.Convex.Cone.Basic
public import Mathlib.Analysis.LocallyConvex.Separation
public import Mathlib.Geometry.... |
4,372 | lean_file_chunk | b723a7d589c25b7e803d80e4fcd5a61b0f9d1527ea53e0c307218e94845bbd79 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
module
public import Mathlib.Analysis.Convex.Extreme
public import Mathlib.Analysis.Convex.StrictConvexSpace
import Mathlib.Algebra.CharP.Invertible
/-! # Extreme points... |
3,413 | lean_file_chunk | 367c330d6383cb81efa9d7252b9ebb1908e7d24823e4706bd2542d14fe53f61e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
module
public import Mathlib.Analysis.Convex.SpecificFunctions.Basic
public import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
/-!
# Convexity properties of `rpo... |
7,074 | lean_file_chunk | 944dfdda33062fa0980857024262692296a3b611d287106f030332b1ae974a8a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel
-/
module
public import Mathlib.Analysis.Calculus.Deriv.ZPow
public import Mathlib.Analysis.SpecialFunctions.Sqrt
public import Mathlib.Analysis.Sp... |
10,609 | lean_file_chunk | ab8756f546f665e065df1b8636a8286a0dcd1a036efe6f7666b00c0eb3fcc8a9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Heather Macbeth
-/
module
public import Mathlib.Analysis.Convex.Slope
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import Mathl... |
9,575 | lean_file_chunk | 6263d9b139101a10946dbb71901491dbd872498e3e52933e9a193a7345d40148 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.AlgebraicTopology.SimplicialComplex.Basic
public import Mathlib.Analysis.Convex.Hull
public import Mathlib.Linea... |
4,312 | lean_file_chunk | 22430bd90338e6fa5c4aeb76e45870fc4e087d66ecb213e868c1261f2f0b3d36 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Mathlib.Analysis.Convex.Combination
public import Mathlib.Analysis.Convex.SimplicialComplex.Basic
public import Mathlib.LinearAlgebra.Finsupp.Vect... |
7,119 | lean_file_chunk | cd13c0d92a770e79ace4238d681e2f8818170dd8b431b13305b369b7fe96e234 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.MellinTransform
public import Mathlib.Analysis.SpecialFunctions.Gamma.Basic
/-!
# Derivative of the Gamma function
This file ... |
2,054 | lean_file_chunk | 39d340a9d5db670555b77eb05e552f5c58ba3cbb699c96b7f7b993dfdac2fc97 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Analysis.Meromorphic.Complex
public import Mathlib.NumberTheory.Harmonic.GammaDeriv
/-!
# The digamma function
This file defines the... |
22,886 | lean_file_chunk | deb4f363031a02f777090a85b9f11d9a8708f9f45820e651cb3da5c2cfff91ad | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.ImproperIntegrals
public import Mathlib.MeasureTheory.Integral.ExpDecay
/-!
# The Gamma function
This file d... |
21,668 | lean_file_chunk | 713243c72fe7461007b434a6f92cb3a61e44ca83745df2928d82a8a8303a1924 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Gamma.Deriv
public import Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral
/-! # Convexity propert... |
8,418 | lean_file_chunk | 20091a90ad2154b807b7ed66fb916bc5cdd8d502e1f470189eee4f74c1ba81e3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Gamma.Beta
/-!
# Deligne's archimedean Gamma-factors
In the theory of L-series one frequently encounters the... |
23,926 | lean_file_chunk | eee3906708a6814867a5e8f55caabea5aa2ea15f3179e438d1d4fb72ce97339d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Convolution
public import Mathlib.Analysis.SpecialFunctions.Complex.LogBounds
public import Mathlib.Analysis.SpecialFunctions.T... |
3,786 | lean_file_chunk | c6cfb2528a609ed299d8ffeb8e887f2e16f999a7ecc6f4cb92e84b8e4419b0f5 | lean_source_file | pkg_mathlib_source_file_chunks | theorem differentiable_one_div_Gamma : Differentiable ℂ fun s : ℂ => (Gamma s)⁻¹ := fun s ↦ by
rcases exists_nat_gt (-s.re) with ⟨n, hs⟩
induction n generalizing s with
| zero =>
rw [Nat.cast_zero, neg_lt_zero] at hs
suffices ∀ m : ℕ, s ≠ -↑m from (differentiableAt_Gamma _ this).inv (Gamma_ne_zero this)
... |
5,096 | lean_file_chunk | 2b5e27e18e5041978571d529516f31fe14b639ce5429c186a0056e2a352fa9e3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Concordance Inc. dba Harmonic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Data.Nat.NthRoot.Defs
public import Mathlib.Tactic.Linarith
public import Mathlib.Tactic.Ring.Basic
public import Mathli... |
18,538 | lean_file_chunk | e5faef8fe85947c78eb6d000662f6953ecf480b729bd1c2016309a884e3654f3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
Rémy Degenne, David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
/-!... |
3,944 | lean_file_chunk | 9041be12f966731ed0430dea63cde4073eddb85c23fe95e2773dedce58b38b8c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
module
public import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
public import Mathlib.MeasureTheory.Integral.Layercake
/-!
# The integral of the real power of a ... |
23,999 | lean_file_chunk | 581e95c4499187c887a2f85070af75274094865efdae478ee0bade4c27f5634a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
Rémy Degenne
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
public import Ma... |
11,204 | lean_file_chunk | cde9dae8c06b7ecc1a404421d755dd765a15bdb30198419cd99db5ae23e2389b | lean_source_file | pkg_mathlib_source_file_chunks | | zero => simp
| succ k IH =>
simp only [Function.iterate_succ', Function.comp_apply, Nat.cast_add, Nat.cast_one, IH]
ext y
simp only [deriv_const_mul_field, deriv_rpow_const, ← mul_assoc, descPochhammer_succ_right,
Polynomial.eval_mul, Polynomial.eval_sub, Polynomial.eval_X, Polynomial.eval_natCast... |
20,052 | lean_file_chunk | 5217a82aed1eb7f2976407ae5dfdadaa287f9a94ac0b1ac94ff103fb05cd5cf7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
Rémy Degenne, David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics... |
11,343 | lean_file_chunk | 3a07ad9940b5bca90d106edbe7f71aac418fd1f23a19603045c58b9a138c5672 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
Rémy Degenne, David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Complex.Log
/-... |
23,989 | lean_file_chunk | 266408dc73215fb9abefa3ae4f3a83b7465acc212a355cf54d06fd2fb83c54eb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
Rémy Degenne, David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public... |
23,975 | lean_file_chunk | c6f66ca75c76dd6e32d3d9e4e4e70c0fb7a642117e35d08d03a66b2d23385dc7 | lean_source_file | pkg_mathlib_source_file_chunks | induction x using recTopCoe
· rcases hy.eq_or_lt with rfl | hy
· rw [rpow_zero, one_mul, zero_add]
rcases hz.eq_or_lt with rfl | hz
· rw [rpow_zero, mul_one, add_zero]
simp [top_rpow_of_pos, hy, hz, add_pos hy hz]
simp [← coe_rpow_of_nonneg, hy, hz, add_nonneg hy hz, NNReal.rpow_add_of_nonneg _ hy h... |
3,359 | lean_file_chunk | b504127e7fdaf8123d7a44a0196ecadf31818203d13d06f14e858070001e4e5c | lean_source_file | pkg_mathlib_source_file_chunks | IsNat (a ^ b) r := by
rcases ha with ⟨rfl⟩
constructor
have : d ≠ 0 := mod_cast hb.den_nz
rw [hb.to_eq rfl rfl, div_eq_mul_inv, NNReal.rpow_natCast_mul, ← Nat.cast_pow, hm, ← hkl, ← hr,
Nat.cast_pow, NNReal.pow_rpow_inv_natCast]
positivity
theorem IsNNRat.nnreal_rpow_isNNRat (a : ℝ≥0) (b : ℝ) (na da : ℕ)... |
23,913 | lean_file_chunk | 9a3c2749b4540eafda28ccca8ca7b944cdd396fbf2c233f5742526f9dd64be74 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
Rémy Degenne, David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Complex
pub... |
23,969 | lean_file_chunk | c93cc214eea622db7f2c43d804843b4a011925416be516ee56c4c7c0c0d3c024 | lean_source_file | pkg_mathlib_source_file_chunks | lemma lt_rpow_inv_iff_of_pos (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 < z) : x < y ^ z⁻¹ ↔ x ^ z < y :=
lt_iff_lt_of_le_iff_le <| rpow_inv_le_iff_of_pos hy hx hz
lemma rpow_inv_lt_iff_of_pos (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 < z) : x ^ z⁻¹ < y ↔ x < y ^ z :=
lt_iff_lt_of_le_iff_le <| le_rpow_inv_iff_of_pos hy hx hz
theo... |
2,150 | lean_file_chunk | d728053a54d848b53ac2b929a85b3c9ef68e291402a8f8ff239d42fc50528899 | lean_source_file | pkg_mathlib_source_file_chunks | let r := (Nat.nthRoot db.natLit! na.natLit!) ^ nb.natLit!
have er : Q(ℕ) := mkRawNatLit r
-- avoid evaluating powers in kernel
let .some ⟨c, pc⟩ ← liftM <| OptionT.run <| evalNatPow er db | failure
let .some ⟨d, pd⟩ ← liftM <| OptionT.run <| evalNatPow na nb | failure
guard (c.natLit! = d.natLit!)
have hcd ... |
23,992 | lean_file_chunk | 7274a8191e119790c8ba80116511daa85932d67050de8682e639e76d184ed552 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Algebra.Module.ZLattice.Summable
public import Mathlib.Analysis.Analytic.Binomial
public import Mathlib.Analysis.Complex.Liouville
public impo... |
23,946 | lean_file_chunk | 9a293f536ea480d4102a202c16d14e5577ef6daf06539d6a0d6e18f45d135a64 | lean_source_file | pkg_mathlib_source_file_chunks | congr! with l
ring
@[simp]
lemma derivWeierstrassP_add_coe (z : ℂ) (l : L.lattice) :
℘'[L] (z + l) = ℘'[L] z := by
simp only [derivWeierstrassP]
rw [← (Equiv.addRight l).tsum_eq]
simp only [← tsum_neg, ← div_neg, Equiv.coe_addRight, Submodule.coe_add, add_sub_add_right_eq_sub]
lemma periodic_derivWeierstr... |
632 | lean_file_chunk | d077be05aa4f7d61f583088857656a2b600a653e3e89d791368090cfbdf7e9ff | lean_source_file | pkg_mathlib_source_file_chunks | private lemma relation_eq_zero : L.relation = 0 := by
ext x
have : Differentiable ℂ L.relation := fun x ↦ (L.analyticAt_relation x).differentiableAt
exact (this.apply_eq_apply_of_bounded (IsZLattice.isCompact_range_of_periodic L.lattice _
this.continuous fun z w hw ↦ by lift w to L.lattice using hw; simp).isB... |
17,386 | lean_file_chunk | 2d2475e2ad5ae9651f3f3a2cc6ec3786ac4d71fe298e4dfaef3e139f657d7c39 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral
public import Mathlib.Analysis.Complex.CauchyIntegral
public import Mathlib.Me... |
6,308 | lean_file_chunk | 81880d6e0b994ffc855c2952471a29a9241c1c5640a12baf2eca7346876aa628 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform
public import Mathlib.Analysis.Fourier.PoissonSummation
/-!
# Poisson summation app... |
18,599 | lean_file_chunk | 1fe70c749b8a9d1231296b89d65e3d47aedd153f495406f3e62deadf280b3b54 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Analysis.SpecialFunctions.Gamma.Basic
public import Mathlib.Analysis.SpecialFunctions.PolarCoord
public import Mathlib.Analysis.Co... |
23,962 | lean_file_chunk | bc83514b2a73b4afd35ef3b489ad5d88c52ab6c305665dcecf874c90a66ab668 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Order.Monotone.Odd
public import Mathlib.Analysis.Calculus.LogDeriv
publi... |
5,307 | lean_file_chunk | 7a7abce44165349c35f73d072214fa7396d4e633030804ff38de1efd60f489cb | lean_source_file | pkg_mathlib_source_file_chunks | DifferentiableWithinAt ℝ (fun x => Real.cosh (f x)) s x :=
hf.hasFDerivWithinAt.cosh.differentiableWithinAt
@[simp, fun_prop]
theorem DifferentiableAt.cosh (hc : DifferentiableAt ℝ f x) :
DifferentiableAt ℝ (fun x => Real.cosh (f x)) x :=
hc.hasFDerivAt.cosh.differentiableAt
theorem DifferentiableOn.cosh (hc ... |
20,147 | lean_file_chunk | 2e840b5cf3d064239a9c24bb06ca21f2a7b50ee9216924f8511f474c57dd3ecb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
public import Mathlib.Topol... |
17,073 | lean_file_chunk | 63b08d901b96974f88f44a801328a224ece796eeddb2aec5e48893cc504b5b4d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex
import Mathlib.Topology.O... |
6,239 | lean_file_chunk | 353b0107153cd376c5afc8dd1239d98024d3d6fc1e6bae7d6607f90db5883c8c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Yaël Dillies
-/
module
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Analysis.SpecialFunctions.Exponential
/-!
# Trigonometric functions as sum... |
23,966 | lean_file_chunk | 556bf002f678bd3fa05ab1f44a25bee52a411135e4b90f167e681108db135211 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
public import Mathlib.Analysis.Normed.Group.AddCircle
public import Mathlib.Algebra.CharZero.Quo... |
14,394 | lean_file_chunk | 28fb251c537b3f0a8a0be0b61111edc0c50242a4f920c5c4ce2ebaec6e9117d1 | lean_source_file | pkg_mathlib_source_file_chunks | simp only [← cos_pos_iff_abs_toReal_lt_pi_div_two, cos_add_pi] at hθ hψ
grind
lemma two_zsmul_eq_iff_eq_of_abs_toReal_lt_pi_div_two {θ ψ : Angle} (hθ : |θ.toReal| < π / 2)
(hψ : |ψ.toReal| < π / 2) : (2 : ℤ) • θ = (2 : ℤ) • ψ ↔ θ = ψ := by
simp_rw [two_zsmul, ← two_nsmul, two_nsmul_eq_iff_eq_of_abs_toReal_lt_p... |
23,998 | lean_file_chunk | a20937e2878d3dd1e8fce032e9f42f40d2e58c7fc8ae1ee294ce266c75880680 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Analysis.Calculus.LogDeriv
public import Mathlib.Analysis.SpecialFunction... |
2,619 | lean_file_chunk | 2a42750ac720dff92fd0fae7e2bb38426c4af445c3216c70759ed38b13f9bb91 | lean_source_file | pkg_mathlib_source_file_chunks | theorem DifferentiableAt.sin (hc : DifferentiableAt ℝ f x) :
DifferentiableAt ℝ (fun x => Real.sin (f x)) x :=
hc.hasFDerivAt.sin.differentiableAt
theorem DifferentiableOn.sin (hc : DifferentiableOn ℝ f s) :
DifferentiableOn ℝ (fun x => Real.sin (f x)) s := fun x h => (hc x h).sin
@[simp, fun_prop]
theorem ... |
1,623 | lean_file_chunk | 3bbdfcd4d7cf9cd4236304d3e463fc5905263e34199e92e587e257649bc519c8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Xuanji Li. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xuanji Li
-/
module
public import Mathlib.Analysis.Meromorphic.Basic
public import Mathlib.Analysis.Meromorphic.NormalForm
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Der... |
7,145 | lean_file_chunk | e26962c655cf8e879aac54233bbd3d9e22a164779c76db19fbfafabb73fd5278 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse
public import Mathlib.Ana... |
23,974 | lean_file_chunk | 93b4e5861b95c489975c49f38697c9b253fdcf8a9e4a01f3a7cdf989cea4928c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Algebra.Field.NegOnePow
public import Mathlib.Algebra.Field.Periodic
publ... |
20,865 | lean_file_chunk | 3c05965f5336ab645fbcb6a07cb18290b4ed6bda4b228b991068f4d9edb66ea4 | lean_source_file | pkg_mathlib_source_file_chunks | linarith [sqrtTwoAddSeries_nonneg le_rfl n]
theorem sin_sq_pi_over_two_pow (n : ℕ) :
sin (π / 2 ^ (n + 1)) ^ 2 = 1 - (sqrtTwoAddSeries 0 n / 2) ^ 2 := by
rw [sin_sq, cos_pi_over_two_pow]
theorem sin_sq_pi_over_two_pow_succ (n : ℕ) :
sin (π / 2 ^ (n + 2)) ^ 2 = 1 / 2 - sqrtTwoAddSeries 0 n / 4 := by
rw [si... |
2,538 | lean_file_chunk | 07cf400ffb9fb7b1ca42535db830726bd3cfb27c34dc008bf389923bd482a2c4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds
public import Mathlib.Analysis.Calculus.DSlope
/-!
# Sinc function
This file contains the d... |
13,471 | lean_file_chunk | 03eae81c277bfad536fdb3c14cd1e289caa44871ccb9cff8d5be4c44032a748c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Algebra.QuadraticDiscriminant
public import Mathlib.Analysis.SpecialFunct... |
7,607 | lean_file_chunk | 9ab0e78cba04aaffb1d8972a9be3ca3884817e67dd182ec9bf7bd546b6f1b1dc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan
public import Mathlib.Anal... |
19,368 | lean_file_chunk | 96bec34dfc46d58091b75016726b8c5c141314f3334b2a8f22904e87a7931e34 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.Calculus.IteratedDeriv.WithinZpow
public import Mathlib.Analysis.Complex.UpperHalfPlane.Exp
public import Mathlib.Analysis.Comp... |
2,538 | lean_file_chunk | 98a0f97cd3a1bcf029bf138a0f9eac72d3feec83a83baa0e03b5353c90ccbc7c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex
public import Mathlib.Ana... |
147 | lean_file_chunk | 4ff0e3f8a3f6c5137641a4cfb5fe9c2c7b4bc720a95135e8034d0b329ff70b9c | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic
deprecated_module (since := "2025-12-15") |
14,829 | lean_file_chunk | cc648713cafd628d0f426a39787aa93ba9b7dd8e3e4207ded08eebf2c706ea2a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
public import Mathlib.MeasureTheory.Integral.PeakFunction
/-! # Euler's infinite product for ... |
11,436 | lean_file_chunk | 45da7393abcd1a2af741c4b4bf7b94881bcfbde1b7e96d934a2ee1330676ba48 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler, Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Analysis.Convex.SpecificFunctions.Deriv
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan... |
6,918 | lean_file_chunk | 19a29f6057d30c9c550851bad3d6cf4bcbabcd8c8721ac5d540c078f494f533e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Geoffrey Irving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Geoffrey Irving
-/
module
public import Mathlib.Analysis.Analytic.Composition
public import Mathlib.Analysis.Analytic.Constructions
public import Mathlib.Analysis.Complex.CauchyInteg... |
6,664 | lean_file_chunk | fc69e39194605feeb78d7e6d9a59b32583e53404a32b76e0027a27997296ebea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
module
public import Mathlib.Analysis.SpecialFunctions.Complex.LogBounds
import Mathlib.Algebra.Order.Interval.Set.Group
/-!
# Complex arctangent
This file defines the com... |
5,847 | lean_file_chunk | 10b5775a557a596e91aa76e4e2814b21bfbeec802a4b26deb4b92e1c7f7ad556 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Fabrizio Barroero. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Fabrizio Barroero, Christopher Hoskin
-/
module
public import Mathlib.Analysis.SpecialFunctions.Complex.Log
public import Mathlib.Order.Interval.Set.Defs
/-!
# ci... |
23,948 | lean_file_chunk | 6d68bbb6cb8160d8533b4f914f39d05a92611ea291133f47478c541236f25924 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle
public import Mathlib.Analy... |
4,535 | lean_file_chunk | 8f830ab13d421b04fdd86d558940a7262d5debd9e62a13b63a6e4d1383d304cb | lean_source_file | pkg_mathlib_source_file_chunks | refine IsOpen.eventually_mem ?_ (⟨hx_re, hx_im⟩ : x.re < 0 ∧ x.im < 0)
exact
IsOpen.and (isOpen_lt continuous_re continuous_zero) (isOpen_lt continuous_im continuous_zero)
theorem arg_eq_nhds_of_im_pos (hz : 0 < im z) : arg =ᶠ[𝓝 z] fun x => Real.arccos (x.re / ‖x‖) :=
((continuous_im.tendsto _).eventually (lt... |
19,934 | lean_file_chunk | 85f8ce8086af8b5d92023c2bf85687d1e959fc6120eb5d5b3397af6db47cdc79 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Analysis.Complex.Convex
public import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
public import Mathlib.Analysis.Calculus.Deriv.Shif... |
5,894 | lean_file_chunk | 24a40dfab7c84d117311969afb68eee46b677a57b3759048477c2f447aa838b4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Complex.Circle
public import Mathlib.NumberTheory.LegendreSymbol.AddCharacter
public import Mathlib.RingTheory... |
6,060 | lean_file_chunk | 0abef4f745aa4663b6955d5167f2b5020037e0cacec27e5b468f745baa4cb0b5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv
public import Mathlib.Anal... |
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