Question

Showing $\int_{0}^{\infty}\frac{[\ln(x+1)]^{4}}{x^{2}}dx=\frac{4\pi^{4}}{15}$

score 139 · Answer 1 · 2021-07-15 00:24:00

139

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Showing $\int_{0}^{\infty}\frac{[\ln(x+1)]^{4}}{x^{2}}dx=\frac{4\pi^{4}}{15}$

Published on 15 Jul 2021 - 0:24

score 96 · Answer 2 · 2026-04-08 02:29:22

96

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Can we substitute complex number into gamma function formula

Published on 08 Apr 2026 - 2:29

score 42 · Answer 3 · 2026-04-11 06:10:39

42

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How to solve equation that involves summation and integration both?

Published on 11 Apr 2026 - 6:10

score 58 · Answer 4 · 2021-07-15 23:24:51

58

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Help needed to solve the integral $\int_0^\infty {\frac{{cy\exp({by}){\Gamma}\left[ {0,\frac{y}{b}} \right]}}{{1 + ay}}} dy$

Published on 15 Jul 2021 - 23:24

score 170 · Answer 5 · 2026-03-27 19:10:18

170

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On the integral $\int\limits_{0}^{\infty}x^{s-1}\left(\frac{e^{(1-a)x}}{e^{x}-1}-\frac{1}{x}\right)\,dx$

Published on 27 Mar 2026 - 19:10

score 82 · Answer 6 · 2026-04-12 06:53:24

82

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Integration of product of lower incomplete gamma function with exponential function?

Published on 12 Apr 2026 - 6:53

score 123 · Answer 7 · 2021-07-17 20:25:28

123

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How to find $\mathrm{\sum_{n=1}^\infty E_{n}(n)= \lim_{k\to\infty}\int_1^\infty \frac{e^{kt+t}t^k-e^t}{e^{kt+2t}t^{k+1}-e^{kt+t}t^k}dt=.26929…}$?

Published on 17 Jul 2021 - 20:25

score 56 · Answer 8 · 2026-03-28 07:48:19

56

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$\lim_{n\to\infty} \sum_{k=0}^{n}(-1)^k\frac{\binom{n}{k}}{ak+b}; a>0,b>0$

Published on 28 Mar 2026 - 7:48

score 53 · Answer 9 · 2026-04-12 00:33:41

53

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How to solve this integration involving lower incomplete gamma function?

Published on 12 Apr 2026 - 0:33

score 211 · Answer 10 · 2026-03-26 11:18:35

211

Views

Computing $\text{PV}\, \int_0^\infty (-1)^{\lfloor x\rfloor}\ln\left(\frac{\sqrt{x}\,e^x\,\Gamma(x)}{\sqrt{2\pi}\,x^x}\right)\,\mathrm{d}x$

Published on 26 Mar 2026 - 11:18

score 123 · Answer 11 · 2021-07-23 19:38:11

Is there any special function that can be related to a generalized falling factorial as the gamma function relates to the ordinary falling factorial?

score 131 · Answer 12 · 2021-07-24 06:40:45

131

Views

Change of Limits of Integration in $\Gamma(\frac{1}{2})$ Using Polar Coordinates

Published on 24 Jul 2021 - 6:40

score 144 · Answer 13 · 2026-04-11 00:15:29

144

Views

Euler's definition of Gamma function

Published on 11 Apr 2026 - 0:15

score 19.7k · Answer 14 · 2026-04-09 17:15:01

19.7k

Views

Why does "Turn! Turn! Turn!" equal 241217.524881?

Published on 09 Apr 2026 - 17:15

score 132 · Answer 15 · 2026-04-10 18:49:48

132

Views

convergence in representation of the Gamma function

Published on 10 Apr 2026 - 18:49

List Question

Showing $\int_{0}^{\infty}\frac{[\ln(x+1)]^{4}}{x^{2}}dx=\frac{4\pi^{4}}{15}$

Can we substitute complex number into gamma function formula

How to solve equation that involves summation and integration both?

Help needed to solve the integral $\int_0^\infty {\frac{{cy\exp({by}){\Gamma}\left[ {0,\frac{y}{b}} \right]}}{{1 + ay}}} dy$

On the integral $\int\limits_{0}^{\infty}x^{s-1}\left(\frac{e^{(1-a)x}}{e^{x}-1}-\frac{1}{x}\right)\,dx$

Integration of product of lower incomplete gamma function with exponential function?

How to find $\mathrm{\sum_{n=1}^\infty E_{n}(n)= \lim_{k\to\infty}\int_1^\infty \frac{e^{kt+t}t^k-e^t}{e^{kt+2t}t^{k+1}-e^{kt+t}t^k}dt=.26929…}$?

$\lim_{n\to\infty} \sum_{k=0}^{n}(-1)^k\frac{\binom{n}{k}}{ak+b}; a>0,b>0$

How to solve this integration involving lower incomplete gamma function?

Computing $\text{PV}\, \int_0^\infty (-1)^{\lfloor x\rfloor}\ln\left(\frac{\sqrt{x}\,e^x\,\Gamma(x)}{\sqrt{2\pi}\,x^x}\right)\,\mathrm{d}x$

Is there any special function that can be related to a generalized falling factorial as the gamma function relates to the ordinary falling factorial?

Change of Limits of Integration in $\Gamma(\frac{1}{2})$ Using Polar Coordinates

Euler's definition of Gamma function

Why does "Turn! Turn! Turn!" equal 241217.524881?

convergence in representation of the Gamma function

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