Question

Closed form for $\sum_{k=0}^\infty \frac{x^{2 k+1}}{(2k+1) \Gamma (\frac{2k+1}{q})}$

score 140 · Answer 1 · 2026-03-27 16:27:49

140

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Closed form for $\sum_{k=0}^\infty \frac{x^{2 k+1}}{(2k+1) \Gamma (\frac{2k+1}{q})}$

Published on 27 Mar 2026 - 16:27

score 44 · Answer 2 · 2019-08-08 20:38:58

44

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Representing the gamma function as an infinite sum

Published on 08 Aug 2019 - 20:38

score 80 · Answer 3 · 2019-08-08 23:18:08

80

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Poles of the gamma function in the zeta functional equation

Published on 08 Aug 2019 - 23:18

score 63 · Answer 4 · 2019-08-09 11:21:35

63

Views

Does the gamma function have unique integer solutions?

Published on 09 Aug 2019 - 11:21

score 116 · Answer 5 · 2019-08-11 18:49:55

116

Views

Upper bound of the fraction of gamma functions

Published on 11 Aug 2019 - 18:49

score 66 · Answer 6 · 2026-03-27 05:39:10

66

Views

Simplifying an alternating sum of a product of factorials

Published on 27 Mar 2026 - 5:39

score 137 · Answer 7 · 2019-08-12 22:34:59

137

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How was this formula made by Srinavasa Ramanujan derived?

Published on 12 Aug 2019 - 22:34

score 74 · Answer 8 · 2019-08-15 13:58:38

74

Views

Representation of gamma function

Published on 15 Aug 2019 - 13:58

score 119 · Answer 9 · 2019-08-15 20:09:06

119

Views

Show that $\sum\limits_{k=1}^{+\infty}[\frac{1}{k}-\frac{1}{k+t}]$ is uniformly-convergent

Published on 15 Aug 2019 - 20:09

score 122 · Answer 10 · 2019-08-17 21:18:33

122

Views

Zeta and gamma function

Published on 17 Aug 2019 - 21:18

score 200 · Answer 11 · 2026-03-27 07:20:09

200

Views

Using Limits to extend the Factorials to Real numbers (and decimals)

Published on 27 Mar 2026 - 7:20

score 52 · Answer 12 · 2019-08-20 15:24:50

Is this : ${\Gamma(1-\alpha)}\int_{0}^\infty \frac{e^{-t}}{{(1+xt)}^{(1-\alpha)}} dt = \int_0^\infty \frac{t^{-\alpha}e^{-t}}{{(1+xt)}} dt$ true?

score 19 · Answer 13 · 2019-08-24 15:23:16

19

Views

Where am I going wrong in simplifying this expression with gamma functions?

Published on 24 Aug 2019 - 15:23

score 419 · Answer 14 · 2019-08-28 03:22:53

419

Views

Evaluate $\int_0^{\infty } \Bigl( 2qe^{-x}-\frac{\sinh (q x)}{\sinh \left(\frac{x}{2}\right)} \Bigr) \frac{dx}x$

Published on 28 Aug 2019 - 3:22

score 235 · Answer 15 · 2019-08-29 01:53:08

235

Views

Binets second loggamma formula

Published on 29 Aug 2019 - 1:53

List Question

Closed form for $\sum_{k=0}^\infty \frac{x^{2 k+1}}{(2k+1) \Gamma (\frac{2k+1}{q})}$

Representing the gamma function as an infinite sum

Poles of the gamma function in the zeta functional equation

Does the gamma function have unique integer solutions?

Upper bound of the fraction of gamma functions

Simplifying an alternating sum of a product of factorials

How was this formula made by Srinavasa Ramanujan derived?

Representation of gamma function

Show that $\sum\limits_{k=1}^{+\infty}[\frac{1}{k}-\frac{1}{k+t}]$ is uniformly-convergent

Zeta and gamma function

Using Limits to extend the Factorials to Real numbers (and decimals)

Is this : ${\Gamma(1-\alpha)}\int_{0}^\infty \frac{e^{-t}}{{(1+xt)}^{(1-\alpha)}} dt = \int_0^\infty \frac{t^{-\alpha}e^{-t}}{{(1+xt)}} dt$ true?

Where am I going wrong in simplifying this expression with gamma functions?

Evaluate $\int_0^{\infty } \Bigl( 2qe^{-x}-\frac{\sinh (q x)}{\sinh \left(\frac{x}{2}\right)} \Bigr) \frac{dx}x$

Binets second loggamma formula

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