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Feb
25
revised How can I demonstrate that $x-x^9$ is divisible by 30?
capitalization, info from comments, titles should be self-contained
Feb
25
revised ${\gcd(n,m)\over n}{n\choose m}$ is an integer
added 111 characters in body
Feb
24
comment Entire function vanishing at $n+\frac{1}{n}$ for $n\geq 1$.
@rubik: If you substitute $\sqrt{x}^2$ for $x$, I think it stops being entire again...
Feb
24
comment Entire function vanishing at $n+\frac{1}{n}$ for $n\geq 1$.
@rubik: $g(x)=\frac{x+\sqrt{x^2-4}}{2}$ is the inverse function to $n+1/n$, so it seemed natural to look for things involving $\sin(\pi g(x))$. Unfortunately $\sin(\pi g(x))$ on its own is not entire, so I played around until I found a factor I could multiply it by that would straighten out the branch points at $\pm 2$.
Feb
23
revised Entire function vanishing at $n+\frac{1}{n}$ for $n\geq 1$.
added 31 characters in body
Feb
23
revised Entire function vanishing at $n+\frac{1}{n}$ for $n\geq 1$.
added 252 characters in body
Feb
23
comment Entire function vanishing at $n+\frac{1}{n}$ for $n\geq 1$.
@Glougloubarbaki: Why do you say that?
Feb
23
answered Entire function vanishing at $n+\frac{1}{n}$ for $n\geq 1$.
Feb
20
comment What happens to the exponential generating function if the sequence is “stretched”?
You may want to read about generalized hypergeometric functions. If $E(z)$ is already such a function, say $E(z)={}_pF_q(a_1,\dots,a_p;b_1,\dots,b_q;z)$, then so are all its stretched versions, more or less. If you stretch by $k$, then assuming I've done my algebra right you get the function $E_k(z)={}_pF_{q+k}(a_1,\dots,a_p;b_1,\dots,b_q,\frac{1}{k+1},\frac{2}{k+1},\dot‌​s ,\frac{k}{k+1};\left(\frac{z}{k+1}\right)^{k+1})$. This probably doesn't help in general, though...
Feb
20
comment What happens to the exponential generating function if the sequence is “stretched”?
@flonk: The answer for $\frac{1}{1-x}$ doesn't lead to the answer for general $E(x)$ (to the best of my knowledge). However, if there was a nice relationship in general, it would certainly be true of $\frac{1}{1-x}$ in particular. My claim is that the particular functions you get don't look like they could possibly come from a nice general relationship.
Feb
19
comment What happens to the exponential generating function if the sequence is “stretched”?
It seems unlikely to me. Note that the $2$-stretch sends $\frac{1}{1-x}$ to a complicated expression involving the Gaussian error function. And WolframAlpha can't even do its $3$-stretch.
Feb
19
revised How can I prove that Cx will intersect x^2
edited tags
Feb
16
reviewed Reopen How would I find $f(x+h)$ for $f(x)=4-x^2$?
Feb
15
reviewed Leave Closed Analytical methods for solving polynomial
Feb
5
reviewed Reviewed How to find the limit of $\frac{\tan(2x)}{\sin(3x)}$ as $x$ approaches $0$ analytically?
Feb
5
reviewed Reviewed small o and big O
Feb
5
reviewed Reopen Is this proof of $a^{1/2}$ being either integer or irrational circular/incorrect?
Feb
5
awarded  Steward
Feb
5
reviewed Leave Closed How do I integrate $\int_0^{2\pi} [x\sin x]\,dx $, where $[\cdot]$ is the greatest integer function?
Feb
5
reviewed Leave Closed Prove that the group algebras $\mathbb{C}Q_8$ and $\mathbb{C}D_4$ are isomorphic.