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If you look at [this previous problem][1], I asked how to find the sum of all the areas between two taxicab geometry circles. However, upon learning about [$\ell^p$ norms][2], I thought it would be pretty interesting to extend the problem to all $\ell^p$ norm circles, not just $\ell^1$ (taxicab).
If $p=1$, then the ... |
Let us say that a Rubik's cube in a particular configuration is in a particular "state". All other configurations of this cube (other "states"), which can be achieved by rotations of the cube can be thought to be connected to each other... rotations are like walking the edges of the graph where the different states are... |
Ultrafinitism is basically resource-bounded constructivism: proofs have constructive content, and what you get out of these constructions isn't much more than you put in.
Looking at the universal and existential quantifier should help clarify things. Constructively, a universally quantified sentence means that if ... |
The web is littered with any number of pages ([example][1]) giving an existence and uniqueness proof that a pair of squares can be found summing to primes congruent to 1 mod 4 (and also that there are no such pairs for primes congruent to 3 mod 4).
However, none of the stuff I've read on the topic offers any help wi... |
For a more fun treatment, Greg Egan touched on this in one of his best short stories, "Luminous" in the collection of the same name. A pair of researchers discover an apparent "defect" in mathematics:
> "You still don't get it, do you,
> Bruno? You're still thinking like a
> Platonist. The universe has only been
... |
I am having a little trouble understanding some results from a program i wrote. I think i have the correct results but i need to understand the theory behind it a little more (i am a programmer, not mathematician).
My program generates symmetric k-regular graphs (single undirected edges). It generates an adjacency m... |
I have the following assertion in my notes from last year that I'm trying hard to digest, but I think it isn't true:
> If $p$ is prime $\Leftrightarrow$ if $p | ab$ then either $p | a$ or $p | b$ or both.
A valid proof must prove both directions, so:
1. if $p$ is prime, let $a_p$ be the prime factorisation of... |
In practice this comes to the same algorithm as Moron's, but I'll give
my two penn'orth anyway. There are two stages: (i) find $z$ with $z^2\equiv -1$
(mod $p$), and (ii) use $z$ to find $x$ and $y$.
Stage (i). If $a$ is a quadratic nonresidue modulo $p$ then $a^{(p-1)/2}
\equiv-1$ (mod $p$) so we can take $z\equ... |
In practice this comes to the same algorithm as Moron's, but I'll give
my two penn'orth anyway. There are two stages: (i) find $z$ with $z^2\equiv -1$
(mod $p$), and (ii) use $z$ to find $x$ and $y$.
Stage (i). If $a$ is a quadratic nonresidue modulo $p$ then $a^{(p-1)/2}
\equiv-1$ (mod $p$) so we can take $z\equ... |
If you look at [this previous problem][1], I asked how to find the sum of all the areas between two taxicab geometry circles. However, upon learning about [$\ell^p$ norms][2], I thought it would be pretty interesting to extend the problem to all $\ell^p$ norm circles, not just $\ell^1$ (taxicab).
If $p=1$, then the ... |
Let G = A *_C B be an amalgamated free product of groups.
My question is: suppose C and G are finitely generated, can we prove that so is A?
I've been trying to prove it by contradiction. Any suggestion?
Thanks... |
Let $G = A *_C B$ be an amalgamated free product of groups.
My question is: suppose $C$ and $G$ are finitely generated, can we prove that so is $A$?
I've been trying to prove it by contradiction. Any suggestion?
Thanks... |
As it is required for most students who wish to do a Ph.D in maths in the US to sit the GRE subject specific mathematics exam, I hope this question will be of interest to the mathematical community and will not be closed.
Essentially, the exam was "rescaled" (made more difficult) in 2001 and I have only been able to... |
There are variations on the problem where the division is always possible and a proof using complete induction.
The first variation is: [..original problem ...] where at least one of the sticks is >=2n.
The second variation is: [..original problem ...] where it is allowed to glue two of the sticks together and ... |
$\sum_{i=1}^{10} \frac{\varphi(n)}{n}$ where $\varphi(n)$ is 1 if the variable $\text n$ has the number $\text 7$ in its typical base-$\text10$ representation, and $\text0$ otherwise.
I am supposed to find out if this series converges or diverges. I think it diverges, and here is why.
We can see that there is a ... |
$\sum_{n=1}^{\infty} \frac{\varphi(n)}{n}$ where $\varphi(n)$ is 1 if the variable $\text n$ has the number $\text 7$ in its typical base-$\text10$ representation, and $\text0$ otherwise.
I am supposed to find out if this series converges or diverges. I think it diverges, and here is why.
We can see that there i... |
Looks okay to me. The first graph is two disjoint copies of C_3 whereas the second graph is C_6. They are not isomorphic and they receive a different canonical label (which is correct). And there's no other 2-regular simple graphs on 6 vertices. The permutation listed is applied to the rows and columns of the matri... |
$\sum_{n=1}^{\infty} \frac{\varphi(n)}{n}$ where $\varphi(n)$ is 1 if the variable $\text n$ has the number $\text 7$ in its typical base-$\text10$ representation, and $\text0$ otherwise.
I am supposed to find out if this series converges or diverges. I think it diverges, and here is why.
We can see that there i... |
If the order of a group is pqr with p q r primes, then there exist three elements A B C with order p q r. Is it possible that the order of the subgroup generated by A and B has the order of pqr ? |
Suppose $V, V'$ are subspaces of dimension $d$ of a vector space $X$. Then there is a subspace $W$ of $X$ of codimension $d$ such that $W \cap V = W \cap V' = \{ 0 \}$.
This can be proved by choosing an explicit basis for $X$ which contains a basis for $V$ and a basis for $V'$ and a basis for $V \cap V'$. On the oth... |
I was wondering what are the differences and relations:
between geometry and topology;
between differential geometry and differential topology;
between algebraic geometry and algebraic topology?
For example:
Are they studying different objects? Such as different mathematical structures/spaces?
if... |
Does the basis of an Euclidean space have to be ordered by definition? Or can be left unordered?
I was also wondering about what is the mapping that can preserve all the structures on Euclidean spaces? Is it [Euclidean transformation][1] (rigid transformation), consisting of rotation, translation and reflection? Or ... |
Your question is quite vague. There are two parallel dynamics that go on when you learn mathematics. On one level, mathematics is extremely specific so as you learn one subject in detail it appears as if all you know is that subject and there appears to be no relation to any other subject. But once you get to underst... |
Is a triangle (its sides and the region enclosed by its sides) in a 2D Euclidean space $\mathbb{E}^2$ a manifold? I was thinking to use the identity mapping as its charts, but for each point on the sides of the triangle, there is no neighborhood of it can be mapped to an open subset in $\mathbb{E}^2$.
Thanks! |
is triangle a manifold ? |
Does the basis of an Euclidean space have to be ordered by definition? Or can be left unordered?
I was also wondering about what is the morphism (i.e. the mapping that can preserve all the structures) on Euclidean spaces? Is it [Euclidean transformation][1] (rigid transformation), consisting of rotation, translation... |
As a supplement to Ryan's answer:
Differential geometry typically studies Riemannian metrics on manifolds, and properties of them. A typical differential geometry result is the *sphere theorem*, stating that if $M$ is a closed manifold equipped with a Riemannian metric for which the sectional curvatures lie in the ... |
As a supplement to Ryan's answer:
Differential geometry typically studies Riemannian metrics on manifolds, and properties of them. A typical differential geometry result is the *sphere theorem*, stating that if $M$ is a closed manifold equipped with a Riemannian metric for which the sectional curvatures lie in the ... |
So if I'm given $H$, when I can conclude there is a group $G$ such that $H\cong G/Z(G)$? It's easy to show that non-trivial cyclic groups are *not* of this form. More generally, any group with the property that all finitely generated subgroups are cyclic (e.g. $\mathbb{Q},\mathbb{Q}/\mathbb{Z}$) cannot be of this form.... |
When can a (finite) group be written as the quotient of some other group by its center? |
I had this question on the exam and boy did it stump me. It was simple to understand why it was true, but I tried several different paths and got nowhere.
Any ideas? |
So I wanted to figure out a meaningful probability for the card deck order problem. I chose arbitrary values in an attempt to show the magnitude of permutations:
> If you and everyone on the Earth right
> now shuffled a million randomized
> decks every millisecond that universe
> has existed, the probability tha... |
Probability of card decks being in the same order for N shufflers over X amount of time? |
### On bases
Bases do not have to be ordered. I respectfully present the following as a counterpoint to Agustí Roig's response.
First of all, a basis is simply a *set* of vectors, by definition; and sets are unordered. If you wish to enumerate the vectors in a basis, you will of course do so in *some* order, but ... |
### On bases
Bases do not have to be ordered. I respectfully present the following as a counterpoint to Agustí Roig's response.
First of all, a basis is simply a *set* of vectors, by definition; and sets are unordered. If you wish to enumerate the vectors in a basis, you will of course do so in *some* order, but ... |
This began as a reply to Jyotirmoy's comment on Agustí's answer, but it became way too long.
As I stated in my comment on Agustí's answer, some textbooks define a basis as a set, and I think this is wrong. Obviously, some people disagree (just read some of the other answers and comments). I'll try to explain why a ... |
I have a problem with the binomial coefficient $\binom{5}{7}$. I know that the solution is zero, but I have problems to reproduce that:
${\displaystyle \binom{5}{7}=\frac{5!}{7!\times(5-7)!}=\frac{5!}{7!\times(-2)!}=\frac{120}{5040\times-2}=\frac{120}{-10080}=-\frac{1}{84}}$
Where is my mistake? |
The definition of the Mandelbrot set that most enthusiasts first encounter is that of the set of all complex numbers $c$ for which the sequence $z_{n+1} = z_n^2 + c$ starting from $z_0 = 0$ does not diverge. For convenience, let us name this familiar quadratic map $P_c(z) = z^2 + c$.
I have read that an equivalent d... |
Why are these two definitions of the Mandelbrot set equivalent? |
what is the useness in math, I know it can provide topological invariant, any other things? |
In this <a href="http://math.stackexchange.com/questions/5896/an-interesting-series/5903#5903">answer</a> to a question about a series, a theorem was stated:
if $A= \\{a_i \\}$ is a set such that $\sum_{i = 1}^{\infty} \frac{1}{a_i}$ converges, then $d(A) = 0$, where $d(A)$ is the <a href="http://en.wikipedia.org/wi... |
### On bases
Bases do not have to be ordered. I respectfully present the following as a counterpoint to Agustí Roig's response.
First of all, a basis is simply a *set* of vectors, by definition; and sets are unordered. If you wish to enumerate the vectors in a basis, you will of course do so in *some* order, but ... |
Suppose
> P(Z|X) = A
> P(Z|Y) = B
where X and Y are independent. How does one determine P(Z|X,Y)?
I haven't studied maths in years, so what I post below may be entirely off base, but I don't like to ask a question without some attempt, so:
From what I read, Baye's theorem is used to calculate update a pr... |
`(4 / (3 - sqrt(5)) ^ 2 - ((6 - 5 * sqrt(6)) / (5 - sqrt(6))) ^ 2 = 2 * sqrt(61 + 24*sqrt(5)`
How to prove it is right equality?
I come up with `(16 / (14 - 6*sqrt(5)) - 6 = 2 * sqrt(61 + 24*sqrt(5)`, but still can't get it to the obvious equality.
Any ideas? |
How to prove it? |
`(4 / (3 - sqrt(5))) ^ 2 - ((6 - 5 * sqrt(6)) / (5 - sqrt(6))) ^ 2 = 2 * sqrt(61 + 24*sqrt(5))`
$$\left(\frac{4}{3-\sqrt{5}}\right)^2 - \left(\frac{6 - 5 \sqrt{6}}{5 - \sqrt{6}}\right)^2 = 2\sqrt{61+24\sqrt{5}}$$
How to prove it is right equality?
I come up with `(16 / (14 - 6*sqrt(5))) - 6 = 2 * sqrt(61 + 24*... |
$$
\left( \frac{4}{(3-\sqrt{5})^2} \right) - \left( \frac{6-5\sqrt{6}}{5-\sqrt{6}} \right)^2 =
2\sqrt{61 + 24 \sqrt{5}}
$$
How to prove it is right equality?
I come up with
$$
\frac{16}{14 -6\sqrt{5}} - 6 = 2 \sqrt{61 +24 \sqrt{5}}
$$
but still can't get it to the obvious equality.
Any ideas? |
`(4 / (3 - sqrt(5))) ^ 2 - ((6 - 5 * sqrt(6)) / (5 - sqrt(6))) ^ 2 = 2 * sqrt(61 + 24*sqrt(5))`
$$\left(\frac{4}{3-\sqrt{5}}\right)^2 - \left(\frac{6 - 5 \sqrt{6}}{5 - \sqrt{6}}\right)^2 = 2\sqrt{61+24\sqrt{5}}$$
How to prove it is right equality?
I come up with `(16 / (14 - 6*sqrt(5))) - 6 = 2 * sqrt(61 + 24*... |
I need to find the exact solution for the lateral surface area of the solid generated by revolving the region bounded by y=x^2, y=0, x=0, and x=sqrt(2) about the X axis.
I have come up with my own solution, but I'm not sure if it's right.
Before substituting values back in, I got
pi/16 (((1+4x^2)^(3/2))2x - (3... |
As it is required for most students who wish to do a Ph.D in maths in the US to sit the GRE subject specific mathematics exam, I hope this question will be of interest to the mathematical community and will not be closed.
Essentially, the exam was "rescaled" (made more difficult) in 2001 and I have only been able to... |
I need to find the exact solution for the lateral surface area of the solid generated by revolving the region bounded by $y=x^2$, $y=0$, $x=0$, and $x=\sqrt 2$ about the X axis.
I have come up with my own solution, but I'm not sure if it's right.
Before substituting values back in, I got
$$ \frac\pi{16} \left(... |
I believe that if we are given two modules $M,N$ over a ring $R$, and a pairing between them
$M \otimes_R N \to R$, we can construct a perfect pairing $M'\otimes_R N' \to R$ by taking kernels.
Is there a name for this construction?
Thanks. |
is there a name for this construction? (taking a pairing and obtaining a perfect one) |
F **y**(w) >= F **x**(w), for all w. Prove P{**y**<**x**} >= 0.5
I had this question on the exam and boy did it stump me. It was simple to understand why it was true, but I tried several different paths and got nowhere.
Any ideas? |
Are there any positive integer solutions (n,x) to the equation (x)(x+1)=n! except (2,1) and (3,2)?
If not (as I suspect is the case), how do you prove that?
In general, is there a way to approach the Diophantine equation n!=P(x) where P is a polynomial? |
`(4 / (3 - sqrt(5))) ^ 2 - ((6 - 5 * sqrt(6)) / (5 - sqrt(6))) ^ 2 = 2 * sqrt(61 + 24*sqrt(5))`
$$\left(\frac{4}{3-\sqrt{5}}\right)^2 - \left(\frac{6 - 5 \sqrt{6}}{5 - \sqrt{6}}\right)^2 = 2\sqrt{61+24\sqrt{5}}$$
How to prove it is right equality?
I come up with $\dfrac{16}{14-6\sqrt{5}}-6=2\sqrt{61+24\sqrt{5}... |
If $\phi:X\rightarrow Y$ is a rational map of varieties, why is the graph of $\phi$ well-defined? That is, if $\langle \rho,U\rangle$ and $\langle \psi,V\rangle$ are two representatives of $\phi$ (so that $U,V\subseteq X$ open, and $\rho\vert_{U\cap V}=\psi\vert_{U\cap V}$), why is the closure of the image of $\rho$ eq... |
Why is the graph of a rational map independent of the choice of representative? |
I suspect this is easy, but that I'm missing something obvious: If a ring homomorphism $f:R\rightarrow S$ is such that a maximal ideal $m$ in $S$ does not have $f^{-1}(m)$ maximal in $R$, must there be some non-unit element $x\in R$ whose image under $f$ is a unit in $S$? I imagine $f^{-1}(m)+(x)$ is minimal over $f^{-... |
Is the failure of MaxSpec to be functorial due to homomorphisms which take non-units to units? |
- If $A$ is a differential one form then $A\wedge A .. (more\text{ }than\text{ }2\text{ }times) = 0$ Then how does the $A\wedge A \wedge A$ make sense in the Chern-Simon's form, $Tr(A\wedge dA + \frac{2}{3} A \wedge A \wedge A)$ ?
- $A$ and $B$ are vector bundle valued differential forms (like say the connectio... |
I suspect this is easy, but that I'm missing something obvious: If a ring homomorphism $f:R\rightarrow S$ is such that a maximal ideal $m$ in $S$ does not have $f^{-1}(m)$ maximal in $R$, must there be some non-unit element $x\in R$ whose image under $f$ is a unit in $S$?
My intuition is just that some "localization... |
I play a game known as bejewel (I'm sure some of you have heard of it) which has the following properties:
> Given a planer graph with every vertex having degree 4 any path of 3 (or more) contiguous colors is considered "complete." Additionally, any two adjacent vertices may be "swapped" to produce said path. If s... |
What is the minimal coloring of a planer graph with swaps? |
Can anyone explain how to do these types of questions for me? I am having trouble wrapping my head around it. Thanks.
A spherical soap bubble is seen to undergo oscillations when slightly deformed. Assuming
that the frequency of these oscillations is a function of the surface tension S of the soap bubble,
the size... |
- If $A$ is a differential one form then $A\wedge A .. (more\text{ }than\text{ }2\text{ }times) = 0$ Then how does the $A\wedge A \wedge A$ make sense in the Chern-Simon's form, $Tr(A\wedge dA + \frac{2}{3} A \wedge A \wedge A)$ ?
I guess this anti-commutative nature of wedge product does not work for Lie algebr... |
- If $A$ is a differential one form then $A\wedge A .. (more\text{ }than\text{ }2\text{ }times) = 0$ Then how does the $A\wedge A \wedge A$ make sense in the Chern-Simon's form, $Tr(A\wedge dA + \frac{2}{3} A \wedge A \wedge A)$ ?
I guess this anti-commutative nature of wedge product does not work for Lie algebr... |
My friend is taking a course on probabilities and come across a problem that has a solution we both have trouble understanding:
A single printer prints, on average, 22 jobs an hour. Let's use a simplification where no job takes more than 2 minutes to complete. Using these assumptions, calculate the upper limit for t... |
Using Poisson distribution to estimate if a printer is available? (I have the solution but don't understand it) |
Dimensional Analysis says ignore the variables you have and manipulate what you've got in terms of dimensions. For example, let any measure of $mass=M$, let any measure of $length=L$, let any measure of $time=T$. $Force=F=MLT^-2$.
Then surface tension is $\frac{MT^2}{L}$. Radius is simple, it is L whilst density is... |
Here is the question for my homework:
A mother wants to invest 7000 USD for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $420.00, how mu... |
I assume you have in your earlier steps:
\\[ \sigma = 2\pi \int_0^\sqrt{2} x^2 \sqrt{1+4x^2} dx \\]
\\[ \tan \theta = 2x \\; \mathrm{and} \\; \sec \theta = \sqrt{1+4x^2} \\]
\\[ \sigma = \frac{\pi}2 \int_{x=0}^{x=\sqrt{2}} \sec^3\theta \tan^2\theta d\theta. \\]
So you have a messy antiderivative you worked ... |
Note that $|G\times H|=|G||H|=nm$; so $G\times H$ is cyclic if and only if there is an element of order $nm$ in $G\times H$.
In any group $A$, if $a,b\in A$ commute with one another, $a$ has order $k$, and $b$ has order $\ell$ then the order of $ab$ will divide lcm$(k,\ell)$ (prove it).
Now take an element of $G\... |
Say I have the square root of 2 over 8. How would I convert this to a mixed radical where the radicand is a **whole number**?
I can convert the square root of 8 to a mixed radical easily (2 sqrt 2) but this fraction is tripping me up. |
Let n = p^k be a power of a prime. Let G be a transitive permutation group on n letters. Show that there exists a fixed-point free element of order p.
I can show that there must be a fixed point:
The transitivity of the group implies that there is only 1 orbit. Burnside's lemma then implies that the average number o... |
What do you mean by the radicand is a "whole number"? In your example $\sqrt{8}=2\sqrt{2}$ in both sides of the equation the radicand is a whole number.
In any case, it doesn't really matter because the problem as you stated it doesn't have a radical at all when you simplify: $\sqrt{\frac{2}{8}}=\sqrt{\frac{1}{4}}=\... |
Say I have the square root of 2 over 9. How would I convert this to a mixed radical where the radicand is a **whole number**?
I can convert the square root of 8 to a mixed radical easily (2 sqrt 2) but this fraction is tripping me up. |
Greg Egan has some fun with this idea in one of his best short stories, "Luminous" (published in the collection of the same name). A pair of researchers are exploring an apparent "defect" in mathematics:
> "You still don't get it, do you,
> Bruno? You're still thinking like a
> Platonist. The universe has only be... |
Say I have the square root of 2/9. How would I convert this to a mixed radical where the radicand is a **whole number**?
I can convert the square root of 8 to a mixed radical easily (2 sqrt 2) but this fraction is tripping me up. |
My question:
A cashier has a total of 114 bills, made up of tens and hundreds. The total value of the money is 6450 USD. How much of each kind does he have?
He has [BLANK] tens and [BLANK] hundreds.
I'm pretty sure there is an algebra equation for this. There is the hard way of doing it on paper (that takes l... |
My question:
A cashier has a total of 114 bills, made up of tens and hundreds. The total value of the money is 6450 USD. How much of each kind does he have?
He has [BLANK] tens and [BLANK] hundreds.
I'm pretty sure there is an algebra equation for this. There is the hard way of doing it on paper (that takes l... |
$\sqrt{\frac{2}{9}} = \frac{\sqrt{2}}{\sqrt{9}} = \frac{\sqrt{2}}{3}$
Is this what you wanted? |
Here is the question for my homework:
A mother wants to invest 7000 USD for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $420.00, how much... |
How to prove an identity in radicals? |
The essence of my question is, if I have a Hermitian matrix that is linearly dependent on a set of parameters and I have an estimate of its eigenvalues, is there a "simple" way to determine the values of the parameters? Ideally, I would also like to have some measure of the goodness of the fit and the degree of variat... |
I'm not sure that I properly understand the question, especially in light of your acceptance of Bill Dubuque's answer and your accompanying comment.
Still, maybe these remarks will be useful:
The map $R/f^{-1}(m) \to S/m$ is a map from an integral domain to a field, and if the
source is not also a field (i.e. if... |
I was reading through some notes on closure operations, and the example was given that for a poset $(S,\preceq)$, the operation on $(\mathcal{P}(S),\subseteq)$ given by $E\mapsto LU(E)$ is a closure operation. Here $LU(E)$ is the set of lower bounds of the upper bounds of $E$ for some $E\subseteq S$. I verified that in... |
Is the union of a family of $LU$-closed sets also $LU$-closed? |
I've seen some of this stuff before, but I'm definitely not an expert. Here's my take (although I'm likely wrong on at least some of it, hopefully not too much):
- You can think of this as a matrix of 1-forms. Then, $A \wedge A$ means "matrix multiplication, where multiplication is wedge product".
- Yes, I thin... |
I was reading through some notes on closure operations, and the example was given that for a poset $(S,\preceq)$, the operation on $(\mathcal{P}(S),\subseteq)$ given by $E\mapsto LU(E)$ is a closure operation. Here $LU(E)$ is the set of lower bounds of the upper bounds of $E$ for some $E\subseteq S$. I verified that in... |
Anybody knows whether there is a list, say first 1000 sphenic numbers? It would be much helpful to know.
Thanks in advance |
How many sphenic numbers are there? |
I was reading through some notes on closure operations, and the example was given that for a poset $(S,\preceq)$, the operation on $(\mathcal{P}(S),\subseteq)$ given by $E\mapsto LU(E)$ is a closure operation. Here $LU(E)$ is the set of lower bounds of the upper bounds of $E$ for some $E\subseteq S$. I verified that in... |
Where can I find a list of sphenic numbers? |
As it is required for most students who wish to do a Ph.D in maths in the US to sit the GRE subject specific mathematics exam, I hope this question will be of interest to the mathematical community and will not be closed.
Essentially, the exam was "rescaled" (made more difficult) in 2001 and I have only been able to... |
I have used logic for specification of security policies in a security model. One of my reviewers asked a question that "why did you used logic and not used algebra for this purpose, and what is your justification?".
The first answer receives in my mind is that algebra is more suitable for using in modeling the behavi... |
At some level, algebra and logic are equivalent. See [Logic as Algebra][1] by Paul Halmos and Steven Givant.
[1]: http://www.amazon.com/gp/product/0883853272?ie=UTF8&tag=theende-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=0883853272 |
How does one find the solution of
$$y^{\prime }\left( 1-\left( 1-t\right) x-x^{2}\right) -\left( 1+h\left( 1+t\right) +x\right) y=0\quad ?$$
$($ In Roger Apéry, *Interpolations de Fractions Continues et Irrationalité de certaines Constantes*, Bull. section des sciences du C.T.H.S., n.º3, p.37-53, the given solut... |
How does one find the solution of
$$y^{\prime }\left( 1-\left( 1-t\right) x-x^{2}\right) -\left( 1+h\left( 1+t\right) +x\right) y=0\quad ?$$
$($ In Roger Apéry, *Interpolations de Fractions Continues et Irrationalité de certaines Constantes*, Bull. section des sciences du C.T.H.S., n.º3, p.37-53, the solution is
... |
I don't like this kind of question —not yours, your referee's— it's enough for authors to solve problems, the existence of other routes that other people might prefer is besides the point, unless there is some relative disadvantage that can the referee can point out.
1. *Is my initial answer to this ques... |
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