Question

Finding the closed form of $ \sum^{\infty}_{m=1} \frac{1}{m} \frac{(-x)^m}{m!}$

score 185 · Answer 1 · 2019-07-26 00:33:19

185

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Finding the closed form of $ \sum^{\infty}_{m=1} \frac{1}{m} \frac{(-x)^m}{m!}$

Published on 26 Jul 2019 - 0:33

score 990 · Answer 2 · 2026-03-27 14:53:38

990

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Closed-form of log gamma integral $\int_0^z\ln\Gamma(t)~dt$ for $z =1,\frac12, \frac13, \frac14, \frac16,$ using Catalan's and Gieseking's constant?

Published on 27 Mar 2026 - 14:53

score 227 · Answer 3 · 2026-03-25 14:25:18

227

Views

On the Clausen triple $8\rm{Cl}_2\left(\frac{\pi}2\right)+3\rm{Cl}_2\left(\frac{\pi}3\right)=12\,\rm{Cl}_2\left(\frac{\pi}6\right)$

Published on 25 Mar 2026 - 14:25

score 78 · Answer 4 · 2026-03-28 05:00:41

78

Views

Proof of an identity connecting a generalized Hypergeometric function to exponential integral.

Published on 28 Mar 2026 - 5:00

score 59 · Answer 5 · 2019-07-30 21:20:25

59

Views

closed formula for: $(g\partial)^n$

Published on 30 Jul 2019 - 21:20

score 535 · Answer 6 · 2019-07-31 09:49:56

535

Views

Examining $\int_0^1 \left(\frac{x - 1}{\ln(x)} \right)^n\:dx$

Published on 31 Jul 2019 - 9:49

score 64 · Answer 7 · 2026-03-25 21:49:48

64

Views

To obtain a closed form for the series related to special functions.

Published on 25 Mar 2026 - 21:49

score 334 · Answer 8 · 2026-03-26 09:38:23

334

Views

Reference request: stability of the Mathieu equation

Published on 26 Mar 2026 - 9:38

score 105 · Answer 9 · 2019-08-01 18:22:14

105

Views

Integrate $I(x) = \frac{1}{ 2 \pi} \int_{-\infty}^{\infty} \frac{e^{-Na}}{jt(1+jt)} e^{\frac{Na}{1+jt}} e^{jxt}dt $

Published on 01 Aug 2019 - 18:22

score 95 · Answer 10 · 2026-03-27 16:24:43

95

Views

Expressing Kummer U function as Meijer G

Published on 27 Mar 2026 - 16:24

score 276 · Answer 11 · 2026-03-25 12:48:35

276

Views

Analytic continuation for special case of Appell's $F_2$ hypergeometric function

Published on 25 Mar 2026 - 12:48

score 152 · Answer 12 · 2026-03-25 20:36:30

152

Views

What is $\oint_{C}z+\cfrac{z}{z+\cfrac{z}{\vdots}}dz?$

Published on 25 Mar 2026 - 20:36

score 221 · Answer 13 · 2026-03-25 09:47:13

221

Views

Curious closed forms of the $q$-Gamma function.

Published on 25 Mar 2026 - 9:47

score 108 · Answer 14 · 2026-02-23 01:17:07

108

Views

Special function related to a nonlinear ODE

Published on 23 Feb 2026 - 1:17

score 91 · Answer 15 · 2019-08-08 10:04:18

91

Views

Indefinite integral involves Meijer G-function

Published on 08 Aug 2019 - 10:04

List Question

Finding the closed form of $ \sum^{\infty}_{m=1} \frac{1}{m} \frac{(-x)^m}{m!}$

Closed-form of log gamma integral $\int_0^z\ln\Gamma(t)~dt$ for $z =1,\frac12, \frac13, \frac14, \frac16,$ using Catalan's and Gieseking's constant?

On the Clausen triple $8\rm{Cl}_2\left(\frac{\pi}2\right)+3\rm{Cl}_2\left(\frac{\pi}3\right)=12\,\rm{Cl}_2\left(\frac{\pi}6\right)$

Proof of an identity connecting a generalized Hypergeometric function to exponential integral.

closed formula for: $(g\partial)^n$

Examining $\int_0^1 \left(\frac{x - 1}{\ln(x)} \right)^n\:dx$

To obtain a closed form for the series related to special functions.

Reference request: stability of the Mathieu equation

Integrate $I(x) = \frac{1}{ 2 \pi} \int_{-\infty}^{\infty} \frac{e^{-Na}}{jt(1+jt)} e^{\frac{Na}{1+jt}} e^{jxt}dt $

Expressing Kummer U function as Meijer G

Analytic continuation for special case of Appell's $F_2$ hypergeometric function

What is $\oint_{C}z+\cfrac{z}{z+\cfrac{z}{\vdots}}dz?$

Curious closed forms of the $q$-Gamma function.

Special function related to a nonlinear ODE

Indefinite integral involves Meijer G-function

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