List questions from polygamma

Published on 01 Sep 2016 - 22:03

132

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Prove or disprove: Is $\psi(x) - \psi(x + y)$ an increasing function of $x > 0$, for all $y > 0$?

Published on 05 Sep 2016 - 19:51

74

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Does the following digamma/trigamma inequality hold? And can it be formally shown?

Published on 14 Oct 2016 - 8:24

141

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Closed form for $\sum_{k\geq 1}\frac{1}{(2^k-1)^a}$

Published on 21 Oct 2016 - 15:19

148

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Convexity of reciprocal polygamma

Published on 08 Nov 2016 - 18:39

89

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Path containing zeros of all derivatives

Published on 11 Nov 2016 - 7:43

961

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Solve the system of equations in the maximum likelihood estimation of Gamma distribution parameters

Published on 26 Dec 2016 - 17:44

384

Views

Asymptotic behavior of Harmonic-like series $\sum_{n=1}^{k} \psi(n) \psi'(n) - (\ln k)^2/2$ as $k \to \infty$

Published on 21 Mar 2026 - 5:42

1k

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Asymptotic expansion of Polygamma functions

Published on 27 Jan 2017 - 16:43

31

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How to sum this vaguely zeta-looking function to QGammafunctions?

Published on 29 Mar 2017 - 15:41

131

Views

Closed form expression for $\psi_{e^{\pi}}^{(3)}(1)$

Published on 18 Feb 2023 - 11:04

143

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Closed form expression for $\psi_{e^{\pi}}^{(3)}(1-i)$

Published on 19 Feb 2023 - 2:16

327

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Closed form expression for an integral

Published on 26 Feb 2023 - 16:50

161

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Integral representation of Bell Polynomial?

Published on 26 May 2023 - 1:36

42

Views

Asymptotic behavior of $\psi^{(n)}(1/2+ix)$ as $n\to\infty$?

Published on 11 Jun 2023 - 23:20

List Question

Relation between the derivative of hurwitz zeta and trigamma

Prove or disprove: Is $\psi(x) - \psi(x + y)$ an increasing function of $x > 0$, for all $y > 0$?

Does the following digamma/trigamma inequality hold? And can it be formally shown?

Closed form for $\sum_{k\geq 1}\frac{1}{(2^k-1)^a}$

Convexity of reciprocal polygamma

Path containing zeros of all derivatives

Solve the system of equations in the maximum likelihood estimation of Gamma distribution parameters

Asymptotic behavior of Harmonic-like series $\sum_{n=1}^{k} \psi(n) \psi'(n) - (\ln k)^2/2$ as $k \to \infty$

Asymptotic expansion of Polygamma functions

How to sum this vaguely zeta-looking function to QGammafunctions?

Closed form expression for $\psi_{e^{\pi}}^{(3)}(1)$

Closed form expression for $\psi_{e^{\pi}}^{(3)}(1-i)$

Closed form expression for an integral

Integral representation of Bell Polynomial?

Asymptotic behavior of $\psi^{(n)}(1/2+ix)$ as $n\to\infty$?

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