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pisco
  • Member for 7 years, 6 months
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11
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
7
Series for $\frac{\log m}{\pi}$ with summands involving harmonic numbers
Dec 10, 2022
answer
7
Three conjectural series for $\pi^2$ and related identities
Oct 16, 2023
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
question
2
Analytic continuation of $\int_V (f(x_1,\cdots,x_n))^s dx_i$
Oct 15
question
2
A property of matrices formed by pairing of roots and coroots
Nov 29
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46
Prove $\sum_{n=1}^\infty\frac{\cot(\pi n\sqrt{61})}{n^3}=-\frac{16793\pi^3}{45660\sqrt{61}}$
44
Remarkable logarithmic integral $\int_0^1 \frac{\log^2 (1-x) \log^2 x \log^3(1+x)}{x}dx$
33
Closed Form for $~\int_0^1\frac{\text{arctanh }x}{\tan\left(\frac\pi2~x\right)}~dx$
32
Conjectural closed-form of $\int_0^1 \frac{\log^n (1-x) \log^{n-1} (1+x)}{1+x} dx$
28
Prove $n! +5$ is not a perfect square for $n\in\mathbb{N}$