Question

Proving that $\sum_{k=0}^\infty\frac{2^{-5k}(6k+1)((2k-1)!!)^3}{4(k!)^3} = {1\over\pi}$

score 186 · Answer 1 · 2026-03-25 16:02:55

186

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Proving that $\sum_{k=0}^\infty\frac{2^{-5k}(6k+1)((2k-1)!!)^3}{4(k!)^3} = {1\over\pi}$

Published on 25 Mar 2026 - 16:02

score 169 · Answer 2 · 2014-10-31 11:16:11

169

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how to integrate $\mathrm{arcsin}\left(x^{15}\right)$?

Published on 31 Oct 2014 - 11:16

score 844 · Answer 3 · 2014-11-11 10:46:22

844

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Hypergeometric function integral representation

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score 1.6k · Answer 4 · 2014-11-19 09:08:34

1.6k

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Simple explanation for Hypergeometric distribution probability

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score 49 · Answer 5 · 2014-11-24 16:50:54

49

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Simplified expression of $ _2F_1((K-1)a,K,Ka,x) $

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score 137 · Answer 6 · 2014-11-29 20:40:21

137

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Evaluate $\int^\pi_{-\pi}(1-a\cos\theta)^{-b-2}\log(1-a\cos\theta)d\theta$

Published on 29 Nov 2014 - 20:40

score 640 · Answer 7 · 2026-03-25 12:52:47

640

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score 139 · Answer 8 · 2014-12-08 03:55:11

139

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an integral involves mutiply of two Kummer Confluent Hypergeometric function

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score 370 · Answer 9 · 2014-12-09 09:00:26

370

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Identities for hypergeometric functions ${}_2F_1$ with z=1/2

Published on 09 Dec 2014 - 9:00

score 90 · Answer 10 · 2026-03-25 14:27:13

90

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Calculate $\int_{0}^t (0.3(1+x)^3+0.7)^{-1/2}\,dx$

Published on 25 Mar 2026 - 14:27

score 47 · Answer 11 · 2026-03-26 01:23:30

47

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Is $\frac{(\alpha)^n (\beta)^n} {(\delta)^n} > \frac{(\alpha+1)^n (\beta+1)^n} {(\delta+1)^n}$ for any $n$ ?(in this specific case)

Published on 26 Mar 2026 - 1:23

score 394 · Answer 12 · 2014-12-16 21:15:35

394

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Any way to simplify integral of Confluent Hypergeometric Function of the First Kind?

Published on 16 Dec 2014 - 21:15

score 299 · Answer 13 · 2014-12-29 05:35:02

299

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asymptotic expansion for Bessel function $I_0(z)$ in terms of Gauss hypergeometric functions ${}_2F_1$

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score 157 · Answer 14 · 2014-12-31 05:00:42

157

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Problems with a Definite Integral Resulting in the Hypergeometric Function

Published on 31 Dec 2014 - 5:00

score 565 · Answer 15 · 2014-12-31 13:11:55

565

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radius of convergence of hypergeometric function

Published on 31 Dec 2014 - 13:11

List Question

Proving that $\sum_{k=0}^\infty\frac{2^{-5k}(6k+1)((2k-1)!!)^3}{4(k!)^3} = {1\over\pi}$

how to integrate $\mathrm{arcsin}\left(x^{15}\right)$?

Hypergeometric function integral representation

Simple explanation for Hypergeometric distribution probability

Simplified expression of $ _2F_1((K-1)a,K,Ka,x) $

Evaluate $\int^\pi_{-\pi}(1-a\cos\theta)^{-b-2}\log(1-a\cos\theta)d\theta$

Identity relating hypergeometric function and Legendre polynomial

an integral involves mutiply of two Kummer Confluent Hypergeometric function

Identities for hypergeometric functions ${}_2F_1$ with z=1/2

Calculate $\int_{0}^t (0.3(1+x)^3+0.7)^{-1/2}\,dx$

Is $\frac{(\alpha)^n (\beta)^n} {(\delta)^n} > \frac{(\alpha+1)^n (\beta+1)^n} {(\delta+1)^n}$ for any $n$ ?(in this specific case)

Any way to simplify integral of Confluent Hypergeometric Function of the First Kind?

asymptotic expansion for Bessel function $I_0(z)$ in terms of Gauss hypergeometric functions ${}_2F_1$

Problems with a Definite Integral Resulting in the Hypergeometric Function

radius of convergence of hypergeometric function

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