List questions from digamma-function

Published on 23 Feb 2026 - 15:29

398

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Show that : $\sum_{k=1}^{\infty}\frac{i^{k(5k+1)}}{k(k+1)}=1-\frac{π}{2}$

Published on 06 May 2019 - 21:52

136

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Find limit of sequence defined by sum of previous terms and harmonics

Published on 25 May 2019 - 17:56

103

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How to solve $\int_0^\infty \frac{\pi^2 e^{-x}}{6x}-\frac{ \operatorname{Li}_2(e^{-x})}{1-e^{-x}}dx$?

Published on 28 May 2019 - 20:48

471

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Help with $-\int_0^1 \ln(1+x)\ln(1-x)dx$

Published on 31 May 2019 - 3:16

160

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psi digamma function

Published on 04 Jun 2019 - 16:55

156

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Prove a tough limit involving the digamma function

Published on 20 Jul 2019 - 6:00

184

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Prove a new digamma finite sum

Published on 12 Mar 2026 - 22:17

86

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Prove $\lim_{n \to \infty} ( \frac{\psi(-1/2+n i )- \psi(-1/2-n i)}{2i}- \frac{n}{n^2+1/4} ) = \frac{\pi}{2}$

Published on 06 Aug 2019 - 9:22

182

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Series involving Digamma relates to Exponential Integral

Published on 23 Sep 2019 - 9:26

130

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Is there a closed form for series of $\sum_k \frac{x^k}{1-x^{2k+1}}$

Published on 28 Sep 2019 - 7:27

324

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Real and imaginary parts of $\ln \Gamma(i b)$

Published on 09 Oct 2019 - 8:37

134

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Evaluation of a digamma series involving golden-ratio

Published on 22 Oct 2019 - 3:14

200

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Compute $\lim_{x\rightarrow 0 }\biggr ( \dfrac{1}{x}\ln (x!)\biggr )$

Published on 25 Oct 2019 - 10:39

141

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ratio of gamma function

Published on 13 Nov 2019 - 12:27

List Question

Uniform convergence of digamma function

Show that : $\sum_{k=1}^{\infty}\frac{i^{k(5k+1)}}{k(k+1)}=1-\frac{π}{2}$

Find limit of sequence defined by sum of previous terms and harmonics

How to solve $\int_0^\infty \frac{\pi^2 e^{-x}}{6x}-\frac{ \operatorname{Li}_2(e^{-x})}{1-e^{-x}}dx$?

Help with $-\int_0^1 \ln(1+x)\ln(1-x)dx$

psi digamma function

Prove a tough limit involving the digamma function

Prove a new digamma finite sum

Prove $\lim_{n \to \infty} ( \frac{\psi(-1/2+n i )- \psi(-1/2-n i)}{2i}- \frac{n}{n^2+1/4} ) = \frac{\pi}{2}$

Series involving Digamma relates to Exponential Integral

Is there a closed form for series of $\sum_k \frac{x^k}{1-x^{2k+1}}$

Real and imaginary parts of $\ln \Gamma(i b)$

Evaluation of a digamma series involving golden-ratio

Compute $\lim_{x\rightarrow 0 }\biggr ( \dfrac{1}{x}\ln (x!)\biggr )$

ratio of gamma function

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