Question

Prove $\lim_{n\mapsto 0}[(\psi(n)+\gamma)\psi^{(1)}(n)-\frac12\psi^{(2)}(n)]=2\zeta(3)$

score 214 · Answer 1 · 2026-03-25 09:28:56

214

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Prove $\lim_{n\mapsto 0}[(\psi(n)+\gamma)\psi^{(1)}(n)-\frac12\psi^{(2)}(n)]=2\zeta(3)$

Published on 25 Mar 2026 - 9:28

score 147 · Answer 2 · 2016-07-10 17:58:25

147

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56

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score 430 · Answer 7 · 2026-03-25 11:10:43

430

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score 538 · Answer 8 · 2016-08-21 01:18:49

538

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Prove this integral $\int_0^\infty \frac{dx}{\sqrt{x^4+a^4}+\sqrt{x^4+b^4}}=\frac{\Gamma(1/4)^2 }{6 \sqrt{\pi}} \frac{a^3-b^3}{a^4-b^4}$

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score 73 · Answer 12 · 2016-09-21 21:55:27

73

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score 277 · Answer 14 · 2026-03-26 12:41:02

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List Question

Prove $\lim_{n\mapsto 0}[(\psi(n)+\gamma)\psi^{(1)}(n)-\frac12\psi^{(2)}(n)]=2\zeta(3)$

Riemann's zeta function in a definite integral

I like to know beta function`s property related with my question

Is there any special property about incomplete beta function $B(x;1-x,x)$?

An integral involving beta function

Closed form for this integral with Beta function $\int_0^\infty x \mathrm B (x,x)~dx$

How can I derive an asymptotic expression for the incomplete Beta function?

Prove this integral $\int_0^\infty \frac{dx}{\sqrt{x^4+a^4}+\sqrt{x^4+b^4}}=\frac{\Gamma(1/4)^2 }{6 \sqrt{\pi}} \frac{a^3-b^3}{a^4-b^4}$

Turning Incomplete Beta Integral to Complete Beta Integral

Trying to Find Closed Form for Beta Integral

A limit involving the Regularized Incomplete Beta Function

Find $c$ such that $cy^3(1-y)^8$ for $0 \leq y \leq 1$ is a PDF

Duplication formula for beta function

Creating a prior function for Bayesian interference of a Bernoulli

Posterior beta from prior beta distribution (features binomial)

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