List questions from polygamma

Published on 22 Mar 2026 - 23:31

271

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The meaning and definition of $\psi^{(-2)}(x)$, and the convergence of some related series involving the Möbius function

Published on 24 Mar 2026 - 5:00

1.5k

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Relation between harmonic series $H(m)$ and polygamma function?

Published on 25 Mar 2026 - 3:11

82

Views

Logarithmic Sum

Published on 25 Mar 2026 - 2:34

172

Views

$\sum_{n=1}^{4000000} \frac{1}{n^3}$ very quick.

Published on 23 Mar 2026 - 1:36

273

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On the series expansion of $\frac{\operatorname{Li}_3(-x)}{1+x}$ and its usage

Published on 20 Mar 2026 - 15:49

363

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Is the polygamma function of order $2$ non-negative (or negative) for all $x >0$?

Published on 24 Mar 2026 - 21:16

267

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Is it possible to simplify $\psi^{(2)}(\frac18)$ or $\psi^{(2)}(\frac pq)$?

Published on 23 Mar 2026 - 0:24

87

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Polygamma expression for $\frac{\Gamma^{(k)}(z)}{\Gamma(z)}$?

Published on 23 Mar 2026 - 0:01

308

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Alternative proof for $\zeta\left(2,\frac14\right)=\psi^{(1)}\left(\frac14\right)=\pi^2+8G$

Published on 23 Mar 2026 - 2:59

75

Views

How to show: $\psi^{(0)}\left(\frac{1}{n}\right) - \psi^{(0)}\left(1 - \frac{1}{n}\right) = -\pi\cot\left(\frac{\pi}{n}\right)$

Published on 23 Mar 2026 - 4:34

443

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Seeking methods to solve: $\int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt$

Published on 18 Mar 2026 - 0:37

294

Views

Dimensional regularization and expansion of gamma function

Published on 22 Mar 2026 - 17:36

175

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Derivative of polygamma function

Published on 22 Mar 2026 - 2:42

731

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Evaluate $\sum_{n=1}^\infty\frac{(-1)^{n-1}H_n}{(2n+1)^3}$

Published on 17 Mar 2026 - 20:44

List Question

Series Representation of Gamma Function

The meaning and definition of $\psi^{(-2)}(x)$, and the convergence of some related series involving the Möbius function

Relation between harmonic series $H(m)$ and polygamma function?

Logarithmic Sum

$\sum_{n=1}^{4000000} \frac{1}{n^3}$ very quick.

On the series expansion of $\frac{\operatorname{Li}_3(-x)}{1+x}$ and its usage

Is the polygamma function of order $2$ non-negative (or negative) for all $x >0$?

Is it possible to simplify $\psi^{(2)}(\frac18)$ or $\psi^{(2)}(\frac pq)$?

Polygamma expression for $\frac{\Gamma^{(k)}(z)}{\Gamma(z)}$?

Alternative proof for $\zeta\left(2,\frac14\right)=\psi^{(1)}\left(\frac14\right)=\pi^2+8G$

How to show: $\psi^{(0)}\left(\frac{1}{n}\right) - \psi^{(0)}\left(1 - \frac{1}{n}\right) = -\pi\cot\left(\frac{\pi}{n}\right)$

Seeking methods to solve: $\int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt$

Dimensional regularization and expansion of gamma function

Derivative of polygamma function

Evaluate $\sum_{n=1}^\infty\frac{(-1)^{n-1}H_n}{(2n+1)^3}$

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