Question

Taylor expansion of $e^t$ starting with $N\geq0$ real number

score 113 · Answer 1 · 2022-03-03 01:26:46

113

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Taylor expansion of $e^t$ starting with $N\geq0$ real number

Published on 03 Mar 2022 - 1:26

score 44 · Answer 2 · 2026-04-10 03:59:19

44

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How to write this integral in terms of Gamma functions

Published on 10 Apr 2026 - 3:59

score 55 · Answer 3 · 2022-03-20 03:20:27

55

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Re-writing Stirling's series

Published on 20 Mar 2022 - 3:20

score 115 · Answer 4 · 2026-03-28 14:44:29

115

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How to evaluate $\int_{0}^{1} \sqrt{\frac{x^{m}}{1-x^{n}}} d x$?

Published on 28 Mar 2026 - 14:44

score 196 · Answer 5 · 2022-03-24 13:14:46

196

Views

Imaginary part of $\log \Gamma$ and when its imarginary argument tends to infinity

Published on 24 Mar 2022 - 13:14

score 205 · Answer 6 · 2022-03-26 15:25:37

205

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Stirling's Approximation of Gamma Function

Published on 26 Mar 2022 - 15:25

score 49 · Answer 7 · 2022-03-28 18:54:34

49

Views

Prove that $\left( \frac{x+1}{k} \right)^x>x!$ for $k<e$

Published on 28 Mar 2022 - 18:54

score 38 · Answer 8 · 2026-04-13 05:40:57

38

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Derivation of a function missing one step in Nandi & Aich, 1994

Published on 13 Apr 2026 - 5:40

score 87 · Answer 9 · 2026-03-26 07:35:30

87

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Show the limit $\lim_{\delta \to 0}\int_{\ln(1+\delta)}^{\delta} \frac{e^{-x}}{x}\,dx \to 0 $ in a proof of the Digamma function

Published on 26 Mar 2026 - 7:35

score 229 · Answer 10 · 2026-04-08 18:38:19

229

Views

Integration of power law distribution and negative arguments in the lower incomplete gamma

Published on 08 Apr 2026 - 18:38

score 131 · Answer 11 · 2026-04-12 22:23:48

131

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Integral involving beta function (continuous version of binomial distribution)

Published on 12 Apr 2026 - 22:23

score 51 · Answer 12 · 2026-04-12 22:24:38

51

Views

Integral representation of the power of a positive number via the gamma function.

Published on 12 Apr 2026 - 22:24

score 1.1k · Answer 13 · 2026-04-09 03:59:40

1.1k

Views

Desmos Factorial function

Published on 09 Apr 2026 - 3:59

score 184 · Answer 14 · 2022-04-12 03:38:19

184

Views

How to find the closed form of $\int_{0}^{\frac{\pi}{2}} \frac{d x}{\left(p \cos ^{2} x+q \sin ^{2} x+r\right)^{n}}$, where $n\in N$?

Published on 12 Apr 2022 - 3:38

score 67 · Answer 15 · 2026-03-28 16:14:15

67

Views

Computing ratio $ \frac{\int_{0}^{1}\left(1-x^{k}\right)^{n} d x}{\int_{0}^{1}\left(1-x^{k}\right)^{n+1}dx} $ by other means than Beta integrals

Published on 28 Mar 2026 - 16:14

List Question

Taylor expansion of $e^t$ starting with $N\geq0$ real number

How to write this integral in terms of Gamma functions

Re-writing Stirling's series

How to evaluate $\int_{0}^{1} \sqrt{\frac{x^{m}}{1-x^{n}}} d x$?

Imaginary part of $\log \Gamma$ and when its imarginary argument tends to infinity

Stirling's Approximation of Gamma Function

Prove that $\left( \frac{x+1}{k} \right)^x>x!$ for $k<e$

Derivation of a function missing one step in Nandi & Aich, 1994

Show the limit $\lim_{\delta \to 0}\int_{\ln(1+\delta)}^{\delta} \frac{e^{-x}}{x}\,dx \to 0 $ in a proof of the Digamma function

Integration of power law distribution and negative arguments in the lower incomplete gamma

Integral involving beta function (continuous version of binomial distribution)

Integral representation of the power of a positive number via the gamma function.

Desmos Factorial function

How to find the closed form of $\int_{0}^{\frac{\pi}{2}} \frac{d x}{\left(p \cos ^{2} x+q \sin ^{2} x+r\right)^{n}}$, where $n\in N$?

Computing ratio $ \frac{\int_{0}^{1}\left(1-x^{k}\right)^{n} d x}{\int_{0}^{1}\left(1-x^{k}\right)^{n+1}dx} $ by other means than Beta integrals

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