List questions from digamma-function

35

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Upper bound of $\left| \sum_{n=1}^N e^{2\pi i\psi(n+1)} \right|$, where $\psi(x)$ is the digamma function

Published on 15 Apr 2026 - 9:46

253

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What about $\int_0^1\frac{\log x}{\log(\gamma+\psi(x+1))}dx$, where $\gamma$ is Euler's constant and $\psi(x)$ the digamma function?

Published on 17 Apr 2026 - 10:42

214

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What's another form of $\sum\limits_{k=1}^\infty{\frac{x^k}{1-y^k}}$?

Published on 14 Apr 2026 - 1:42

128

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An interesting sum arising from a statistics problem

Published on 10 Apr 2026 - 22:55

50

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Euler-Mascheroni constant as local minima of a function

Published on 12 Apr 2026 - 1:46

99

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Derivatives of Polygamma Functions

Published on 10 May 2026 - 23:34

593

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How to evaluate $\int_0^{\pi/2} x\ln^2(\sin x)\textrm{d}x$ in a different way?

Published on 16 Apr 2026 - 20:19

188

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Evaluating an integral using the beta, gamma and digamma functions

Published on 12 Apr 2026 - 0:43

56

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Inequality involving the Gamma function : $e<\frac{\Gamma(x)e^x}{(x-1)^{(x-1)}\sqrt{x}}<e\sqrt{2\pi}$

Published on 15 Apr 2026 - 13:35

34

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Bound on $\sum_{i=1}^n \sum_{k=1}^i \frac{1}{(n-k+1)^2}$

Published on 12 Apr 2026 - 17:46

66

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Pick's theorem and the gamma function?

Published on 14 Apr 2026 - 13:23

56

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Finding digamma at an irrational input

Published on 12 Apr 2026 - 19:28

230

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computing the expected value of gamma function

Published on 12 Apr 2026 - 4:05

244

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

Published on 25 Mar 2026 - 19:04

108

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Derivative of Bessel $K$

Published on 15 Apr 2026 - 23:52

List Question

Upper bound of $\left| \sum_{n=1}^N e^{2\pi i\psi(n+1)} \right|$, where $\psi(x)$ is the digamma function

What about $\int_0^1\frac{\log x}{\log(\gamma+\psi(x+1))}dx$, where $\gamma$ is Euler's constant and $\psi(x)$ the digamma function?

What's another form of $\sum\limits_{k=1}^\infty{\frac{x^k}{1-y^k}}$?

An interesting sum arising from a statistics problem

Euler-Mascheroni constant as local minima of a function

Derivatives of Polygamma Functions

How to evaluate $\int_0^{\pi/2} x\ln^2(\sin x)\textrm{d}x$ in a different way?

Evaluating an integral using the beta, gamma and digamma functions

Inequality involving the Gamma function : $e<\frac{\Gamma(x)e^x}{(x-1)^{(x-1)}\sqrt{x}}<e\sqrt{2\pi}$

Bound on $\sum_{i=1}^n \sum_{k=1}^i \frac{1}{(n-k+1)^2}$

Pick's theorem and the gamma function?

Finding digamma at an irrational input

computing the expected value of gamma function

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

Derivative of Bessel $K$

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