Question

Covariance of $\frac{X}{\|X\|}$ with $X\sim N(\mu, Id)$, and ${}_1F_1(a;b;z)$ properties

score 30 · Answer 1 · 2023-11-01 21:55:00

30

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Covariance of $\frac{X}{\|X\|}$ with $X\sim N(\mu, Id)$, and ${}_1F_1(a;b;z)$ properties

Published on 01 Nov 2023 - 21:55

score 49 · Answer 2 · 2023-11-04 15:14:44

49

Views

A limit with respect to the WZ-pairs $\lim_{N \to \infty} \sum_{k=0}^{\infty} F(N+a,k+b)$

Published on 04 Nov 2023 - 15:14

score 89 · Answer 3 · 2023-11-04 17:07:38

89

Views

Evaluating 3f2 hypergeometric function using Euler integral

Published on 04 Nov 2023 - 17:07

score 36 · Answer 4 · 2023-11-05 10:20:55

36

Views

Hypergeometric functions with constant modulus over the positive real line

Published on 05 Nov 2023 - 10:20

score 46 · Answer 5 · 2026-02-23 15:03:51

46

Views

Tricky "Divergent" Integral: Correction to Groundstate

Published on 23 Feb 2026 - 15:03

score 27 · Answer 6 · 2023-11-15 20:37:46

27

Views

Prove an inequality with confluent hypergeometric functions

Published on 15 Nov 2023 - 20:37

score 37 · Answer 7 · 2023-11-15 20:41:26

37

Views

How and why does $\frac{(k+1)(c+k)}{(a+k)(b+k)}=1+\frac{1+c-a-b}{k}+O\left(\frac{1}{k^2}\right)$ hold for integer $k$ and complex $a,b,c$?

Published on 15 Nov 2023 - 20:41

score 32 · Answer 8 · 2026-03-25 19:00:18

32

Views

Analytic continuation of incomplete beta function

Published on 25 Mar 2026 - 19:00

score 55 · Answer 9 · 2023-11-21 02:57:05

55

Views

Spectrum of Klein-Gordon operator in Hyperbolic space.

Published on 21 Nov 2023 - 2:57

score 97 · Answer 10 · 2023-11-23 01:35:59

97

Views

Asymptotic limit of Hypergeometric function into Whittaker function.

Published on 23 Nov 2023 - 1:35

score 290 · Answer 11 · 2023-11-27 15:51:45

290

Views

Proving $_4F_3\left(\frac{1}{2},\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{5}{4}, \frac{3}{2};1\right)=\frac{\Gamma^8(1/4)}{768\pi^3}$

Published on 27 Nov 2023 - 15:51

score 72 · Answer 12 · 2026-03-29 17:33:57

72

Views

How to prove that $\big(\operatorname{sinc}(x) + \operatorname{sinc}(x-1) \big)^{*r} = \frac{\Gamma{(r+1)}}{\Gamma{(x+1)}\Gamma{(r-x+1)}}$

Published on 29 Mar 2026 - 17:33

score 204 · Answer 13 · 2023-11-29 06:43:56

204

Views

Asymptotic of $\sum_{k=0}^\infty\frac{\Gamma (k+n+1) \Gamma (3 k+n+1)}{\Gamma (k+2) \Gamma (3 k+2 n+2)}$ as $n\to \infty$

Published on 29 Nov 2023 - 6:43

score 49 · Answer 14 · 2023-12-03 02:31:09

49

Views

Proof of transformation of Hypergeometric to Whittaker.

Published on 03 Dec 2023 - 2:31

score 129 · Answer 15 · 2023-12-04 10:34:52

129

Views

Asymptotic Expansions for the Hypergeometric function for large parameters and bounded z?

Published on 04 Dec 2023 - 10:34

List Question

Covariance of $\frac{X}{\|X\|}$ with $X\sim N(\mu, Id)$, and ${}_1F_1(a;b;z)$ properties

A limit with respect to the WZ-pairs $\lim_{N \to \infty} \sum_{k=0}^{\infty} F(N+a,k+b)$

Evaluating 3f2 hypergeometric function using Euler integral

Hypergeometric functions with constant modulus over the positive real line

Tricky "Divergent" Integral: Correction to Groundstate

Prove an inequality with confluent hypergeometric functions

How and why does $\frac{(k+1)(c+k)}{(a+k)(b+k)}=1+\frac{1+c-a-b}{k}+O\left(\frac{1}{k^2}\right)$ hold for integer $k$ and complex $a,b,c$?

Analytic continuation of incomplete beta function

Spectrum of Klein-Gordon operator in Hyperbolic space.

Asymptotic limit of Hypergeometric function into Whittaker function.

Proving $_4F_3\left(\frac{1}{2},\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{5}{4}, \frac{3}{2};1\right)=\frac{\Gamma^8(1/4)}{768\pi^3}$

How to prove that $\big(\operatorname{sinc}(x) + \operatorname{sinc}(x-1) \big)^{*r} = \frac{\Gamma{(r+1)}}{\Gamma{(x+1)}\Gamma{(r-x+1)}}$

Asymptotic of $\sum_{k=0}^\infty\frac{\Gamma (k+n+1) \Gamma (3 k+n+1)}{\Gamma (k+2) \Gamma (3 k+2 n+2)}$ as $n\to \infty$

Proof of transformation of Hypergeometric to Whittaker.

Asymptotic Expansions for the Hypergeometric function for large parameters and bounded z?

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