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pisco
  • Member for 8 years, 5 months
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Top posts

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question
13
Dirichlet series that gives power of $\pi$ at positive even integer
Nov 27
answer
13
How to prove the identity $L(2,(\frac{\cdot}3))=\frac2{15}\sum\limits_{k=1}^\infty\frac{48^k}{k(2k-1)\binom{4k}{2k}\binom{2k}k}$?
Dec 21, 2022
answer
13
A curious hypergeometric series related to Riemann's zeta function
Jan 23
question
11
Identities of Bernoulli numbers from rank 2 simple Lie algebras
Nov 25
answer
10
Three conjectural series for $\pi^2$ and related identities
Oct 16, 2023
answer
8
Series for $\frac{\log m}{\pi}$ with summands involving harmonic numbers
Dec 10, 2022
question
5
Epstein zeta function for non-fundamental discriminant to L-series
May 25, 2023
answer
4
A vanishing sum and related $p$-adic congruences
Nov 3, 2023
question
3
Roots of polynomial $\sum_{\sigma \in W} x^{l(\sigma)}$
Sep 27, 2024
answer
3
How big can the index inside the root lattice of the lattice generated by a subset of roots be?
Nov 19

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57
Prove $\sum_{n=1}^\infty\frac{\cot(\pi n\sqrt{61})}{n^3}=-\frac{16793\pi^3}{45660\sqrt{61}}$
45
Remarkable logarithmic integral $\int_0^1 \frac{\log^2 (1-x) \log^2 x \log^3(1+x)}{x}dx$
35
Closed Form for $~\int_0^1\frac{\text{arctanh }x}{\tan\left(\frac\pi2~x\right)}~dx$
32
Conjectural closed-form of $\int_0^1 \frac{\log^n (1-x) \log^{n-1} (1+x)}{1+x} dx$
30
Prove: $\int_0^2 \frac{dx}{\sqrt{1+x^3}}=\frac{\Gamma\left(\frac{1}{6}\right)\Gamma\left(\frac{1}{3}\right)}{6\Gamma\left(\frac{1}{2}\right)}$