Question

Evalute triple sum $ \sum_{m\geq 0}\sum_{n \geq 0}\sum_{p\geq 0} \frac{m!n!p!}{(m+n+p+2)!}$

score 226 · Answer 1 · 2026-03-28 04:35:41

226

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Evalute triple sum $ \sum_{m\geq 0}\sum_{n \geq 0}\sum_{p\geq 0} \frac{m!n!p!}{(m+n+p+2)!}$

Published on 28 Mar 2026 - 4:35

score 76 · Answer 2 · 2026-03-26 11:24:11

76

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Does this function has a name? (Similar to Beta Function)

Published on 26 Mar 2026 - 11:24

score 289 · Answer 3 · 2026-03-31 01:04:05

289

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find function $f$ such that $f(x)=xf(x-1)$ and $f(1) = 1$

Published on 31 Mar 2026 - 1:04

score 92 · Answer 4 · 2026-03-28 01:07:27

92

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Evaluation of Limit involved in the proof of Asymptotic Unbiasedness of S

Published on 28 Mar 2026 - 1:07

score 138 · Answer 5 · 2026-03-25 15:52:40

138

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What is the value of $\int_{0}^{t} (t-s)^{\alpha-1} (1-s)^{\alpha} \rm{d}s$?, where $0<t<1$ and $0 <\alpha \leq 1$.

Published on 25 Mar 2026 - 15:52

score 641 · Answer 6 · 2026-03-26 11:18:17

641

Views

Integrals related to $\int_0^{\pi} \left(\frac{\sin(\alpha u)^\alpha \sin((1-\alpha) u)^{1-\alpha}}{\sin u} \right)^{\rho/\alpha}du$

Published on 26 Mar 2026 - 11:18

score 79 · Answer 7 · 2020-07-21 16:41:52

79

Views

Compute the following product limit

Published on 21 Jul 2020 - 16:41

score 214 · Answer 8 · 2026-03-25 09:28:56

214

Views

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 143 · Answer 9 · 2026-03-29 08:57:53

Prove $\prod_{n\ge0}^{ }\frac{\left(n+a\right)\left(n+b\right)}{\left(n+c\right)\left(n+d\right)}=\frac{\Gamma(c)\Gamma(d) }{ \Gamma(a)\Gamma(b)}$

score 106 · Answer 10 · 2020-07-23 11:00:27

106

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Summation involving Gamma function

Published on 23 Jul 2020 - 11:00

score 165 · Answer 11 · 2026-03-26 20:37:55

165

Views

Writing out a Maple-integrated Function does not work as intended

Published on 26 Mar 2026 - 20:37

score 98 · Answer 12 · 2020-07-24 07:40:23

98

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Find the area between $f(x) = x^2+3x+7 $ and $g(x) = xe^{x^3+4}$ for $x \in [3,5]$.

Published on 24 Jul 2020 - 7:40

score 68 · Answer 13 · 2026-03-30 18:17:54

68

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Simplification of an expression.

Published on 30 Mar 2026 - 18:17

score 452 · Answer 14 · 2026-03-25 04:39:22

452

Views

How to use Euler-Maclaurin summation to show the following relationship over Gamma function

Published on 25 Mar 2026 - 4:39

score 105 · Answer 15 · 2020-07-27 07:45:01

105

Views

Proving $\int_{0}^\infty \left(\frac{1}{(1+ix)^b}-\frac{1}{(1-ix)^b}\right)\sin(ax)\mathrm{d}x =\frac{-ia^{b-1}e^{-a}\pi}{\Gamma[b]} $

Published on 27 Jul 2020 - 7:45

List Question

Evalute triple sum $ \sum_{m\geq 0}\sum_{n \geq 0}\sum_{p\geq 0} \frac{m!n!p!}{(m+n+p+2)!}$

Does this function has a name? (Similar to Beta Function)

find function $f$ such that $f(x)=xf(x-1)$ and $f(1) = 1$

Evaluation of Limit involved in the proof of Asymptotic Unbiasedness of S

What is the value of $\int_{0}^{t} (t-s)^{\alpha-1} (1-s)^{\alpha} \rm{d}s$?, where $0<t<1$ and $0 <\alpha \leq 1$.

Integrals related to $\int_0^{\pi} \left(\frac{\sin(\alpha u)^\alpha \sin((1-\alpha) u)^{1-\alpha}}{\sin u} \right)^{\rho/\alpha}du$

Compute the following product limit

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

Prove $\prod_{n\ge0}^{ }\frac{\left(n+a\right)\left(n+b\right)}{\left(n+c\right)\left(n+d\right)}=\frac{\Gamma(c)\Gamma(d) }{ \Gamma(a)\Gamma(b)}$

Summation involving Gamma function

Writing out a Maple-integrated Function does not work as intended

Find the area between $f(x) = x^2+3x+7 $ and $g(x) = xe^{x^3+4}$ for $x \in [3,5]$.

Simplification of an expression.

How to use Euler-Maclaurin summation to show the following relationship over Gamma function

Proving $\int_{0}^\infty \left(\frac{1}{(1+ix)^b}-\frac{1}{(1-ix)^b}\right)\sin(ax)\mathrm{d}x =\frac{-ia^{b-1}e^{-a}\pi}{\Gamma[b]} $

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