Question

How to compute: $I_x =\int_0^1 t^x e^{-\frac{1}{1-t^2}} dt~~~x>0$?

score 76 · Answer 1 · 2017-11-04 18:03:52

76

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How to compute: $I_x =\int_0^1 t^x e^{-\frac{1}{1-t^2}} dt~~~x>0$?

Published on 04 Nov 2017 - 18:03

score 280 · Answer 2 · 2017-11-06 00:12:23

280

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last step in gamma function derivation using dominated converge theorem

Published on 06 Nov 2017 - 0:12

score 166 · Answer 3 · 2017-11-07 09:08:48

166

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Characterization of logarithmic derivative of the gamma function

Published on 07 Nov 2017 - 9:08

score 223 · Answer 4 · 2026-03-25 19:00:50

223

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Proof trigamma recurrence relation

Published on 25 Mar 2026 - 19:00

score 48 · Answer 5 · 2017-11-12 19:17:06

48

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Does the following function have any poles or zeros?

Published on 12 Nov 2017 - 19:17

score 74 · Answer 6 · 2017-11-13 08:10:36

74

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Derive the identity $\int_0^{\infty} e^{x^\alpha} dx = \Gamma(\frac{\alpha+1}{\alpha})$

Published on 13 Nov 2017 - 8:10

score 103 · Answer 7 · 2017-11-13 14:10:03

103

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Derive for $z=x+iy$: $|\Gamma(z)| = \Gamma(x) \Pi_{k=0}^\infty \left[1+\frac{y}{(x+k)^2}\right]^{-1/2}$

Published on 13 Nov 2017 - 14:10

score 195 · Answer 8 · 2017-11-14 07:09:26

195

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Does anybody known the relationship between the $\Gamma (a)$ and $\Gamma (a+\frac{1}{2})$

Published on 14 Nov 2017 - 7:09

score 155 · Answer 9 · 2017-11-14 11:09:27

155

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Expressing ${_3F_2}$ in terms of gamma functions

Published on 14 Nov 2017 - 11:09

score 112 · Answer 10 · 2017-11-15 08:32:17

112

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Gamma reflection formula for large z

Published on 15 Nov 2017 - 8:32

score 532 · Answer 11 · 2017-11-16 02:56:07

532

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Where does this formula for the product of Gamma Functions come from?

Published on 16 Nov 2017 - 2:56

score 140 · Answer 12 · 2017-11-21 14:26:34

140

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Is it possible to deduce that the limit $\lim_{x\to-\infty}\sum_{n=1}^\infty\lambda(n)\frac{x^n}{\Gamma(n)}$ is finite?

Published on 21 Nov 2017 - 14:26

score 66 · Answer 13 · 2017-11-21 15:01:01

66

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$\sum_{n=0}^m \binom{m}{n}\Gamma\Big(n-\frac{1}{2}\Big)\Gamma\Big(m-n-\frac{1}{2}\Big)=0$

Published on 21 Nov 2017 - 15:01

score 199 · Answer 14 · 2026-04-07 23:15:29

199

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How to proof with the definition of gamma function?

Published on 07 Apr 2026 - 23:15

score 63 · Answer 15 · 2017-11-28 06:50:05

63

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Calculate $ \int_{0}^{1}\frac{r^{p+1}}{(1-r^{2})^{\frac{p}{2}-\frac{1}{2}}}dr $

Published on 28 Nov 2017 - 6:50

List Question

How to compute: $I_x =\int_0^1 t^x e^{-\frac{1}{1-t^2}} dt~~~x>0$?

last step in gamma function derivation using dominated converge theorem

Characterization of logarithmic derivative of the gamma function

Proof trigamma recurrence relation

Does the following function have any poles or zeros?

Derive the identity $\int_0^{\infty} e^{x^\alpha} dx = \Gamma(\frac{\alpha+1}{\alpha})$

Derive for $z=x+iy$: $|\Gamma(z)| = \Gamma(x) \Pi_{k=0}^\infty \left[1+\frac{y}{(x+k)^2}\right]^{-1/2}$

Does anybody known the relationship between the $\Gamma (a)$ and $\Gamma (a+\frac{1}{2})$

Expressing ${_3F_2}$ in terms of gamma functions

Gamma reflection formula for large z

Where does this formula for the product of Gamma Functions come from?

Is it possible to deduce that the limit $\lim_{x\to-\infty}\sum_{n=1}^\infty\lambda(n)\frac{x^n}{\Gamma(n)}$ is finite?

$\sum_{n=0}^m \binom{m}{n}\Gamma\Big(n-\frac{1}{2}\Big)\Gamma\Big(m-n-\frac{1}{2}\Big)=0$

How to proof with the definition of gamma function?

Calculate $ \int_{0}^{1}\frac{r^{p+1}}{(1-r^{2})^{\frac{p}{2}-\frac{1}{2}}}dr $

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