List questions from digamma-function

33

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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 03 Jan 2018 - 21:41

250

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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 09 Jan 2018 - 10:01

211

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

Published on 19 Oct 2011 - 15:18

125

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An interesting sum arising from a statistics problem

Published on 03 Aug 2020 - 19:56

48

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Euler-Mascheroni constant as local minima of a function

Published on 12 Aug 2020 - 14:41

98

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Derivatives of Polygamma Functions

Published on 25 Mar 2026 - 17:43

588

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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 19 Aug 2020 - 12:34

185

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Evaluating an integral using the beta, gamma and digamma functions

Published on 20 Aug 2020 - 12:46

53

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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 23 Aug 2020 - 14:12

31

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

Published on 28 Aug 2020 - 16:19

63

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Pick's theorem and the gamma function?

Published on 30 Aug 2020 - 4:57

53

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Finding digamma at an irrational input

Published on 29 Sep 2020 - 14:29

227

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computing the expected value of gamma function

Published on 08 Oct 2020 - 12:31

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

105

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Derivative of Bessel $K$

Published on 14 Oct 2020 - 20:50

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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