Question

Asymptotic behavior of the hypergeometric function

score 575 · Answer 1 · 2019-08-30 17:20:54

575

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Asymptotic behavior of the hypergeometric function

Published on 30 Aug 2019 - 17:20

score 151 · Answer 2 · 2019-08-31 13:27:08

151

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Kummer's transformation of the solution in hypergeometric equation

Published on 31 Aug 2019 - 13:27

score 113 · Answer 3 · 2019-09-02 10:04:57

113

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Evaluating hypergeometric function.

Published on 02 Sep 2019 - 10:04

score 73 · Answer 4 · 2026-02-24 00:43:00

73

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Is there a clean relation between the Tricomi function $U(-a,b,z)$ (as a function of its first argument) and an Airy function?

Published on 24 Feb 2026 - 0:43

score 118 · Answer 5 · 2019-09-17 14:09:08

118

Views

How to prove $[x^n]C^m(n)=\binom{2n+m-1}{n}-\binom{2n+m-1}{n-1}$

Published on 17 Sep 2019 - 14:09

score 23 · Answer 6 · 2019-09-20 14:57:39

23

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Hypergeometric when there are 2 subjects

Published on 20 Sep 2019 - 14:57

score 127 · Answer 7 · 2019-09-30 21:33:15

127

Views

Estimate of the hypergeometric function $_3F_2$

Published on 30 Sep 2019 - 21:33

score 143 · Answer 8 · 2014-03-12 22:12:03

143

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Showing that $ { }_2F_1(1, n + 1;n+2; \frac{1}{2}) \in O(2^n)$

Published on 12 Mar 2014 - 22:12

score 24.8k · Answer 9 · 2014-03-15 02:45:10

24.8k

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Crazy $\int_0^\infty{_3F_2}\left(\begin{array}c\tfrac58,\tfrac58,\tfrac98\\\tfrac12,\tfrac{13}8\end{array}\middle|\ {-x}\right)^2\frac{dx}{\sqrt x}$

Published on 15 Mar 2014 - 2:45

score 1.6k · Answer 10 · 2014-03-19 15:42:15

1.6k

Views

Approximating hypergeometric function F(1,1+a,2+a,z) for z->1

Published on 19 Mar 2014 - 15:42

score 101 · Answer 11 · 2014-03-19 21:28:24

Proving $\frac{\cos(t \arctan(\sqrt{x}))}{(1+x)^{t/2}}= \sum_{k \ge 0}\frac{\Gamma(t+2k)\Gamma(k+1)}{\Gamma(t)\Gamma(2k+1)}\frac{(-x)^k}{k!}$

score 3.2k · Answer 12 · 2014-03-28 01:10:46

3.2k

Views

Limit of the hypergeometric function

Published on 28 Mar 2014 - 1:10

score 52 · Answer 13 · 2014-04-15 13:12:35

52

Views

Hypergeometric function relation knowing initial value?

Published on 15 Apr 2014 - 13:12

score 142 · Answer 14 · 2014-04-15 16:51:06

142

Views

Can the hypergeometric function be extended analytically to the complex plane in the interval [1,$\infty$ )?

Published on 15 Apr 2014 - 16:51

score 275 · Answer 15 · 2014-04-17 04:13:01

275

Views

Hypergeometric Function simple identity

Published on 17 Apr 2014 - 4:13

List Question

Asymptotic behavior of the hypergeometric function

Kummer's transformation of the solution in hypergeometric equation

Evaluating hypergeometric function.

Is there a clean relation between the Tricomi function $U(-a,b,z)$ (as a function of its first argument) and an Airy function?

How to prove $[x^n]C^m(n)=\binom{2n+m-1}{n}-\binom{2n+m-1}{n-1}$

Hypergeometric when there are 2 subjects

Estimate of the hypergeometric function $_3F_2$

Showing that $ { }_2F_1(1, n + 1;n+2; \frac{1}{2}) \in O(2^n)$

Crazy $\int_0^\infty{_3F_2}\left(\begin{array}c\tfrac58,\tfrac58,\tfrac98\\\tfrac12,\tfrac{13}8\end{array}\middle|\ {-x}\right)^2\frac{dx}{\sqrt x}$

Approximating hypergeometric function F(1,1+a,2+a,z) for z->1

Proving $\frac{\cos(t \arctan(\sqrt{x}))}{(1+x)^{t/2}}= \sum_{k \ge 0}\frac{\Gamma(t+2k)\Gamma(k+1)}{\Gamma(t)\Gamma(2k+1)}\frac{(-x)^k}{k!}$

Limit of the hypergeometric function

Hypergeometric function relation knowing initial value?

Can the hypergeometric function be extended analytically to the complex plane in the interval [1,$\infty$ )?

Hypergeometric Function simple identity

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