Question

Calculating $S=\sum\limits_{n=1}^\infty\left(\frac{1}{\Gamma^2(n+1)}\right)^{{1}/{n}}$

score 184 · Answer 1 · 2026-03-25 06:05:41

184

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Calculating $S=\sum\limits_{n=1}^\infty\left(\frac{1}{\Gamma^2(n+1)}\right)^{{1}/{n}}$

Published on 25 Mar 2026 - 6:05

score 76 · Answer 2 · 2018-11-29 15:50:54

76

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Can $\int_{-\pi}^\pi e^{\cos(\theta)}\sin(\sin(\theta))\sin(nx)dx=\frac{\pi}{n!}$ be extened to non-integers?

Published on 29 Nov 2018 - 15:50

score 135 · Answer 3 · 2018-11-30 14:37:59

135

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How do I prove $z\Delta(z+1) = \Delta(z)$, where $\Gamma(z)=1/\Delta(z)$?

Published on 30 Nov 2018 - 14:37

score 242 · Answer 4 · 2026-03-25 04:39:00

242

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On an Inequality for the Riemann Zeta Function

Published on 25 Mar 2026 - 4:39

score 48 · Answer 5 · 2018-12-04 00:28:06

48

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A More Direct Proof Please of a Theorem of the Incomplete Gamma Function

Published on 04 Dec 2018 - 0:28

score 280 · Answer 6 · 2026-03-26 04:53:53

280

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How to show that $\left| \Gamma \left(x + iy \right) \right|^{2} \approx (\pi y^{(2x - 1)}) /(\cosh(\pi y))$?

Published on 26 Mar 2026 - 4:53

score 86 · Answer 7 · 2018-12-06 07:38:59

86

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On Ramanujan's proof of Bertrand's postulate (using stirling formula)

Published on 06 Dec 2018 - 7:38

score 59 · Answer 8 · 2018-12-08 08:21:15

59

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Area under the graph of $r\mapsto\binom nr$

Published on 08 Dec 2018 - 8:21

score 343 · Answer 9 · 2018-12-08 11:55:10

343

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Prove that $\prod_{r=1}^m \sin \left( \frac {r\pi}{2m+1}\right) =\frac {\sqrt {2m+1}}{2^m}$

Published on 08 Dec 2018 - 11:55

score 193 · Answer 10 · 2018-12-09 19:45:29

193

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Prove $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}\ln{(2n+1)}}{2n+1}=\pi/4(\gamma-\ln{\pi})+\pi\ln{(\Gamma(3/4))}$

Published on 09 Dec 2018 - 19:45

score 44 · Answer 11 · 2026-03-26 08:03:52

44

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definite integration - solution breakdown

Published on 26 Mar 2026 - 8:03

score 84 · Answer 12 · 2018-12-13 01:32:49

84

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Calculate $E(Y)$ where $Y=X^{1.5}$

Published on 13 Dec 2018 - 1:32

score 117 · Answer 13 · 2026-03-25 15:17:54

117

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Beta distribution: find the parameter $\alpha$ of $\mathcal{B}e(\alpha,\frac{1}{3})$

Published on 25 Mar 2026 - 15:17

score 190 · Answer 14 · 2018-12-15 17:29:38

190

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How to derive the closed form of this gamma quotient?

Published on 15 Dec 2018 - 17:29

score 372 · Answer 15 · 2018-12-16 07:27:59

372

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Seeking Methods to solve $\int_{0}^{\infty} \frac{e^{-x^n}}{x^n + 1}\:dx $

Published on 16 Dec 2018 - 7:27

List Question

Calculating $S=\sum\limits_{n=1}^\infty\left(\frac{1}{\Gamma^2(n+1)}\right)^{{1}/{n}}$

Can $\int_{-\pi}^\pi e^{\cos(\theta)}\sin(\sin(\theta))\sin(nx)dx=\frac{\pi}{n!}$ be extened to non-integers?

How do I prove $z\Delta(z+1) = \Delta(z)$, where $\Gamma(z)=1/\Delta(z)$?

On an Inequality for the Riemann Zeta Function

A More Direct Proof Please of a Theorem of the Incomplete Gamma Function

How to show that $\left| \Gamma \left(x + iy \right) \right|^{2} \approx (\pi y^{(2x - 1)}) /(\cosh(\pi y))$?

On Ramanujan's proof of Bertrand's postulate (using stirling formula)

Area under the graph of $r\mapsto\binom nr$

Prove that $\prod_{r=1}^m \sin \left( \frac {r\pi}{2m+1}\right) =\frac {\sqrt {2m+1}}{2^m}$

Prove $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}\ln{(2n+1)}}{2n+1}=\pi/4(\gamma-\ln{\pi})+\pi\ln{(\Gamma(3/4))}$

definite integration - solution breakdown

Calculate $E(Y)$ where $Y=X^{1.5}$

Beta distribution: find the parameter $\alpha$ of $\mathcal{B}e(\alpha,\frac{1}{3})$

How to derive the closed form of this gamma quotient?

Seeking Methods to solve $\int_{0}^{\infty} \frac{e^{-x^n}}{x^n + 1}\:dx $

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