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4 questions with no upvoted or accepted answers
8
votes
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answers
237
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Sequences for which $\prod (1-z^n)^{a(n)}$ is a polynomial
This is mostly a reference request.
I'm working with complex coefficients, although all I have in mind have integer coefficients.
Let $a=(a(n))_{n\ge 1}$ be a sequence, say of integers (I have non-...
- 63.9k
2
votes
0
answers
159
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Finding similar Zudilin-Cohen recurrence relations and cfracs for $\frac{\zeta(4)}{13}$?
I. Two recurrence relations
The first one was also discussed in this MO post. We have the similar,
\begin{align}
(n+1)^5 u_{n+1} &= (2n + 1)(9n^2 + 9n + 3)(15n^2 + 15n + 4)u_n +3n^3(9n^2-1)u_{n-1}\...
- 12.6k
2
votes
0
answers
222
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Four kinds of generalized hypergeometric formulas for $\pi$
Given,
$$\begin{array}{|c|c|c|c|}
\hline
n&a_n&b_n&c_n\\
\hline
1 & 6541681608 & 163096908 & -640320^3\\
\hline
2 & 85840 & 4492 & -14112^2\\
\hline
3 & 28302 &...
- 12.6k
0
votes
0
answers
356
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Is $\lim_{x\to\infty}\sum_{n=-\infty}^{\infty}\frac{x}{n^2+x^2}=\pi$?
It seems that
$$\lim_{x\to\infty}\sum_{n=-\infty}^{\infty}\frac{x}{n^2+x^2}=\pi.$$
But I can't prove it. I cannot prove that the function is decreasing in $x$ either.
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