Question

Hyperbolic series similar to Ramanujan’s identities

score 223 · Answer 1 · 2026-03-25 12:53:44

223

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Hyperbolic series similar to Ramanujan’s identities

Published on 25 Mar 2026 - 12:53

score 32 · Answer 2 · 2019-06-25 16:01:14

32

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Specific form of an Apell Hypergeometric function with two variables

Published on 25 Jun 2019 - 16:01

score 569 · Answer 3 · 2019-07-02 07:06:04

569

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Closed form for $f(x)=\ _3F_2\left(\tfrac12,\tfrac12,\tfrac12;\tfrac32,\tfrac32;x\right)$

Published on 02 Jul 2019 - 7:06

score 84 · Answer 4 · 2019-07-03 11:09:21

84

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The integral $\int_{0}^{\infty}~ e^{-x}~ \mbox{sech}^2(x+z)~dx,~~ z \in R$

Published on 03 Jul 2019 - 11:09

score 466 · Answer 5 · 2019-07-04 17:28:04

466

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How to Solve Advanced Recurrence Relations

Published on 04 Jul 2019 - 17:28

score 487 · Answer 6 · 2019-07-09 11:35:48

487

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Asymptotic behaviour of generalized hypergeometric function

Published on 09 Jul 2019 - 11:35

score 91 · Answer 7 · 2019-07-09 22:07:42

91

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Prove $\sum _{n \geq 1} \left[\frac{1}{n}-\frac{2}{n+1}{_2F_1}(1,\frac{n+1}{2};\frac{n+3}{2};-1)\right]=\frac{\pi}{4}-\frac{\log 2}{2}$

Published on 09 Jul 2019 - 22:07

score 168 · Answer 8 · 2026-03-25 07:56:49

168

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Evaluate integral using asymptotic methods

Published on 25 Mar 2026 - 7:56

score 365 · Answer 9 · 2019-07-18 14:18:56

365

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A series for $\log (a) \log (b)$ in terms of hypergeometric function

Published on 18 Jul 2019 - 14:18

score 357 · Answer 10 · 2026-03-27 10:12:08

357

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Prove ${_4 F_3} \left(\frac12, \frac12, 1, 1; \frac34, \frac54, \frac32; \frac14 \right)= \frac14 \left(\frac{\pi^2}{4}+\log^2 (2+\sqrt{3} ) \right)$

Published on 27 Mar 2026 - 10:12

score 168 · Answer 11 · 2026-03-25 11:20:11

168

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General expression for polynomials related to ${_2 F_1} (n,n,2n,1-x)$

Published on 25 Mar 2026 - 11:20

score 373 · Answer 12 · 2019-07-25 16:41:15

373

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Integration involving the Gauss 2F1 Hypergeometric Function

Published on 25 Jul 2019 - 16:41

score 384 · Answer 13 · 2019-07-25 18:35:47

384

Views

Closed form for an infinite series involving lower incomplete gamma functions

Published on 25 Jul 2019 - 18:35

score 203 · Answer 14 · 2026-03-26 06:32:40

203

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Conjecture: ${_2 F_1} \left(\frac{1}{2}- \frac{x}{2},1- \frac{x}{2};2;1 \right)=\prod_{n=2}^\infty \frac{(2n-2+x)(2n-1+x)}{2n (2n-3+2x)}$

Published on 26 Mar 2026 - 6:32

score 64 · Answer 15 · 2019-07-29 06:49:30

64

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Sufficient conditions for $\lim_{N \to \infty} \frac{{_2 F_1} (a,b;c+N;z)}{{_2 F_1} (a,b;c+N+1;z)}=1$

Published on 29 Jul 2019 - 6:49

List Question

Hyperbolic series similar to Ramanujan’s identities

Specific form of an Apell Hypergeometric function with two variables

Closed form for $f(x)=\ _3F_2\left(\tfrac12,\tfrac12,\tfrac12;\tfrac32,\tfrac32;x\right)$

The integral $\int_{0}^{\infty}~ e^{-x}~ \mbox{sech}^2(x+z)~dx,~~ z \in R$

How to Solve Advanced Recurrence Relations

Asymptotic behaviour of generalized hypergeometric function

Prove $\sum _{n \geq 1} \left[\frac{1}{n}-\frac{2}{n+1}{_2F_1}(1,\frac{n+1}{2};\frac{n+3}{2};-1)\right]=\frac{\pi}{4}-\frac{\log 2}{2}$

Evaluate integral using asymptotic methods

A series for $\log (a) \log (b)$ in terms of hypergeometric function

Prove ${_4 F_3} \left(\frac12, \frac12, 1, 1; \frac34, \frac54, \frac32; \frac14 \right)= \frac14 \left(\frac{\pi^2}{4}+\log^2 (2+\sqrt{3} ) \right)$

General expression for polynomials related to ${_2 F_1} (n,n,2n,1-x)$

Integration involving the Gauss 2F1 Hypergeometric Function

Closed form for an infinite series involving lower incomplete gamma functions

Conjecture: ${_2 F_1} \left(\frac{1}{2}- \frac{x}{2},1- \frac{x}{2};2;1 \right)=\prod_{n=2}^\infty \frac{(2n-2+x)(2n-1+x)}{2n (2n-3+2x)}$

Sufficient conditions for $\lim_{N \to \infty} \frac{{_2 F_1} (a,b;c+N;z)}{{_2 F_1} (a,b;c+N+1;z)}=1$

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