List questions from polygamma

Published on 03 Nov 2017 - 5:09

192

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Upper bound for the nth derivative of $\Gamma(x)^n$

Published on 01 Aug 2020 - 15:45

97

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Derivatives of Polygamma Functions

Published on 17 Aug 2020 - 21:44

58

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What is the root of $\sum _{i=1}^{m-1} i^k=m^k$ given integer k?

Published on 04 Oct 2020 - 5:51

243

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Is there a decomposition for the digamma function as a sum of digamma functions?

Published on 12 Oct 2020 - 8:56

92

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Polygamma function approximation to infinity

Published on 13 Nov 2020 - 14:03

82

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Partial sum of polygamma

Published on 13 Nov 2020 - 20:39

210

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Another bizarre sum involving a binomial coefficient and inverse powers of integers.

Published on 10 Dec 2020 - 16:13

190

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A convergent series for the Trigamma function $\psi_1(n) =\sum_{k=n}^{\infty} \frac1{k^2} $

Published on 12 Dec 2020 - 4:31

119

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Simplify this expression $e^{\psi\left(\frac12+\frac{i}{2\sqrt{3}}\right)+\psi\left(\frac12-\frac{i}{2\sqrt{3}}\right)}$?

Published on 12 Feb 2021 - 10:38

49

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a limit containing a digamma function

Published on 18 Feb 2021 - 10:19

53

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Is there a general summation formula for the polygamma function at $z=1/2$? i.e $\psi^{(s)}(\frac{1}{2})$ for all s.

Published on 26 Feb 2021 - 6:04

376

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Evaluation of $\sum_{n=1}^{\infty}\frac{1}{n(2n+1)}=2-2\ln(2)$

Published on 20 May 2021 - 11:51

127

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A curious summation.

Published on 21 Mar 2026 - 8:28

59

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closed form in terms of a polygamma function? $ f(2,2)=\sum \sum \exp\big(- n^2k^2 \big)? $

Published on 19 Aug 2021 - 11:20

List Question

Generalized hypergeometric function at unity

Upper bound for the nth derivative of $\Gamma(x)^n$

Derivatives of Polygamma Functions

What is the root of $\sum _{i=1}^{m-1} i^k=m^k$ given integer k?

Is there a decomposition for the digamma function as a sum of digamma functions?

Polygamma function approximation to infinity

Partial sum of polygamma

Another bizarre sum involving a binomial coefficient and inverse powers of integers.

A convergent series for the Trigamma function $\psi_1(n) =\sum_{k=n}^{\infty} \frac1{k^2} $

Simplify this expression $e^{\psi\left(\frac12+\frac{i}{2\sqrt{3}}\right)+\psi\left(\frac12-\frac{i}{2\sqrt{3}}\right)}$?

a limit containing a digamma function

Is there a general summation formula for the polygamma function at $z=1/2$? i.e $\psi^{(s)}(\frac{1}{2})$ for all s.

Evaluation of $\sum_{n=1}^{\infty}\frac{1}{n(2n+1)}=2-2\ln(2)$

A curious summation.

closed form in terms of a polygamma function? $ f(2,2)=\sum \sum \exp\big(- n^2k^2 \big)? $

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