Question

$\int_{0}^{e}\frac{\sin(\operatorname{W(x)})-1}{\sin(\operatorname{W(x)})+1}\frac{\sin(\operatorname{2W(x)})-1}{\sin(\operatorname{2W(x)})+1}dx=?$

score 54 · Answer 1 · 2026-03-26 01:12:37

54

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$\int_{0}^{e}\frac{\sin(\operatorname{W(x)})-1}{\sin(\operatorname{W(x)})+1}\frac{\sin(\operatorname{2W(x)})-1}{\sin(\operatorname{2W(x)})+1}dx=?$

Published on 26 Mar 2026 - 1:12

score 845 · Answer 2 · 2026-03-25 05:11:25

845

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Expressing Hermite polynomials using confluent hypergeometric functions

Published on 25 Mar 2026 - 5:11

score 32 · Answer 3 · 2020-04-04 11:57:52

32

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Is there a closed form expression of $_3F_2\left(a,b,-\frac{1}{2};a-\frac{1}{2},a+b;1\right)$ where $a,b>0$?

Published on 04 Apr 2020 - 11:57

score 22 · Answer 4 · 2020-04-05 00:19:08

22

Views

An integral involving hypergeometric functions and leading to a sum with Gamma functions

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score 64 · Answer 5 · 2026-03-27 05:05:51

64

Views

How to find infinite sum of trigonometric, hyperbolic function?

Published on 27 Mar 2026 - 5:05

score 90 · Answer 6 · 2020-04-08 20:47:28

90

Views

Reduction of ${}_{4}F_{3}(\cdots; 1)$

Published on 08 Apr 2020 - 20:47

score 74 · Answer 7 · 2020-04-09 03:08:22

74

Views

Hypergeometric representation degenerate cases

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score 94 · Answer 8 · 2026-03-28 02:21:26

94

Views

Integral involving Hypergeometric Function 2F1 and its derivative

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score 55 · Answer 9 · 2020-04-14 07:16:11

55

Views

An ODE with Hyperbolic function as solution

Published on 14 Apr 2020 - 7:16

score 192 · Answer 10 · 2020-04-15 22:43:59

192

Views

Closed form of $\sum_{k=0}^{\infty} \sum_{m=0}^{\infty} r^m \cdot t^k \binom{m+k}{k} \binom{m+k+1}{k}$ for fixed $r, t$

Published on 15 Apr 2020 - 22:43

score 380 · Answer 11 · 2020-04-21 19:18:07

380

Views

Value of $\sum_{n=1}^{\infty}\frac{1}{\sqrt{n!}}$?

Published on 21 Apr 2020 - 19:18

score 177 · Answer 12 · 2026-03-25 12:21:16

177

Views

Help with the Euler-type integral $\int_{0}^{m}\frac{1-e^{2\pi i x}}{x-j}\frac{x^{s-1}}{(1+x)^{z}}dx$

Published on 25 Mar 2026 - 12:21

score 328 · Answer 13 · 2026-03-26 04:34:52

328

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What is the probability of drawing at least 1 ace, at least 1 king, and at least 1 queen, in a 5 card poker hand from a standard 52 card deck?

Published on 26 Mar 2026 - 4:34

score 95 · Answer 14 · 2020-04-25 01:45:33

95

Views

What is this mystery function that wolfram alpha says my exponential generating function is equal too?

Published on 25 Apr 2020 - 1:45

score 851 · Answer 15 · 2020-04-27 20:36:52

851

Views

Solution to Laguerre differential equation

Published on 27 Apr 2020 - 20:36

List Question

$\int_{0}^{e}\frac{\sin(\operatorname{W(x)})-1}{\sin(\operatorname{W(x)})+1}\frac{\sin(\operatorname{2W(x)})-1}{\sin(\operatorname{2W(x)})+1}dx=?$

Expressing Hermite polynomials using confluent hypergeometric functions

Is there a closed form expression of $_3F_2\left(a,b,-\frac{1}{2};a-\frac{1}{2},a+b;1\right)$ where $a,b>0$?

An integral involving hypergeometric functions and leading to a sum with Gamma functions

How to find infinite sum of trigonometric, hyperbolic function?

Reduction of ${}_{4}F_{3}(\cdots; 1)$

Hypergeometric representation degenerate cases

Integral involving Hypergeometric Function 2F1 and its derivative

An ODE with Hyperbolic function as solution

Closed form of $\sum_{k=0}^{\infty} \sum_{m=0}^{\infty} r^m \cdot t^k \binom{m+k}{k} \binom{m+k+1}{k}$ for fixed $r, t$

Value of $\sum_{n=1}^{\infty}\frac{1}{\sqrt{n!}}$?

Help with the Euler-type integral $\int_{0}^{m}\frac{1-e^{2\pi i x}}{x-j}\frac{x^{s-1}}{(1+x)^{z}}dx$

What is the probability of drawing at least 1 ace, at least 1 king, and at least 1 queen, in a 5 card poker hand from a standard 52 card deck?

What is this mystery function that wolfram alpha says my exponential generating function is equal too?

Solution to Laguerre differential equation

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