Question

Convergence of geometric mean over arithmetic mean $G_n / A_n$

score 83 · Answer 1 · 2026-03-27 17:52:36

83

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Convergence of geometric mean over arithmetic mean $G_n / A_n$

Published on 27 Mar 2026 - 17:52

score 470 · Answer 2 · 2021-05-30 13:16:15

470

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Prove that $\Gamma(\frac{1}{2}-x)\Gamma(\frac{1}{2}+x)=\frac{\pi}{\cos\pi x}$

Published on 30 May 2021 - 13:16

score 407 · Answer 3 · 2026-04-08 18:42:25

407

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Is $\pi$! irrational?

Published on 08 Apr 2026 - 18:42

score 604 · Answer 4 · 2021-06-05 04:27:00

604

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Sum $\sum_{n=1}^{\infty}\sum_{k=1}^{2n}\frac{(-1)^{n+1}(2\pi)^{2n}}{(2n-k+1)!}\left(\frac{1}{2\pi i}\right)^k$

Published on 05 Jun 2021 - 4:27

score 166 · Answer 5 · 2026-04-11 08:48:31

166

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Some gamma function properties

Published on 11 Apr 2026 - 8:48

score 55 · Answer 6 · 2026-04-12 06:16:16

55

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Non-probabilistic proof for this infinite series identity related to the generalized negative binomial distribution?

Published on 12 Apr 2026 - 6:16

score 73 · Answer 7 · 2021-06-14 13:49:15

73

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Generalization of factorial based on the original combinatorial definition?

Published on 14 Jun 2021 - 13:49

score 122 · Answer 8 · 2021-06-16 10:53:08

122

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What is the real part of $\ln\Gamma(-i z)$

Published on 16 Jun 2021 - 10:53

score 133 · Answer 9 · 2026-04-11 18:57:38

133

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An expansion for $\ln^2\Gamma(x+1)$

Published on 11 Apr 2026 - 18:57

score 97 · Answer 10 · 2026-03-26 12:53:38

97

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Proof the equality $\prod_{r=1}^{mn}\left(x+mn -r\right)=\prod_{k=1}^{m}\prod_{l=1}^{n}\left(x+mn-(1+ml-k) \right)$

Published on 26 Mar 2026 - 12:53

score 103 · Answer 11 · 2026-04-09 19:38:11

103

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How to evaluate $\frac{\partial}{\partial x}\Gamma(f(x))$?

Published on 09 Apr 2026 - 19:38

score 255 · Answer 12 · 2021-06-26 01:53:05

255

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Critique of this proof of $\frac{1}{\Gamma(s)} = s \prod_{n = 1}^\infty \frac{\left(1 + \frac{s}{n}\right)}{\left(1+ \frac{1}{n}\right)^s}$

Published on 26 Jun 2021 - 1:53

score 448 · Answer 13 · 2021-06-28 17:40:47

448

Views

Upper bound on Trigamma function $\psi^{(1)}(x)$ for $x\in\Bbb N$

Published on 28 Jun 2021 - 17:40

score 124 · Answer 14 · 2026-04-05 08:13:15

124

Views

Can we make any positive integer from one $4$ and a finite number of $\lfloor x\rfloor$, $\Gamma$ and $\sqrt{}$?

Published on 05 Apr 2026 - 8:13

score 93 · Answer 15 · 2021-06-29 20:09:22

93

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Asymptotic behavior of $\frac{\Gamma \left(2-\frac{1}{p}\right) \Gamma (t+1)}{\Gamma \left(t-\frac{1}{p}+2\right)}$

Published on 29 Jun 2021 - 20:09

List Question

Convergence of geometric mean over arithmetic mean $G_n / A_n$

Prove that $\Gamma(\frac{1}{2}-x)\Gamma(\frac{1}{2}+x)=\frac{\pi}{\cos\pi x}$

Is $\pi$! irrational?

Sum $\sum_{n=1}^{\infty}\sum_{k=1}^{2n}\frac{(-1)^{n+1}(2\pi)^{2n}}{(2n-k+1)!}\left(\frac{1}{2\pi i}\right)^k$

Some gamma function properties

Non-probabilistic proof for this infinite series identity related to the generalized negative binomial distribution?

Generalization of factorial based on the original combinatorial definition?

What is the real part of $\ln\Gamma(-i z)$

An expansion for $\ln^2\Gamma(x+1)$

Proof the equality $\prod_{r=1}^{mn}\left(x+mn -r\right)=\prod_{k=1}^{m}\prod_{l=1}^{n}\left(x+mn-(1+ml-k) \right)$

How to evaluate $\frac{\partial}{\partial x}\Gamma(f(x))$?

Critique of this proof of $\frac{1}{\Gamma(s)} = s \prod_{n = 1}^\infty \frac{\left(1 + \frac{s}{n}\right)}{\left(1+ \frac{1}{n}\right)^s}$

Upper bound on Trigamma function $\psi^{(1)}(x)$ for $x\in\Bbb N$

Can we make any positive integer from one $4$ and a finite number of $\lfloor x\rfloor$, $\Gamma$ and $\sqrt{}$?

Asymptotic behavior of $\frac{\Gamma \left(2-\frac{1}{p}\right) \Gamma (t+1)}{\Gamma \left(t-\frac{1}{p}+2\right)}$

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