Question

On the representation $\Gamma(z)=\sum_{n=2}^\infty \int_0^\infty a(n)e^{-e^{nx}}e^{nzx}dx$, for arithmetic functions $a(n)$ and $\Re z>0$

score 204 · Answer 1 · 2026-03-26 13:01:00

204

Views

On the representation $\Gamma(z)=\sum_{n=2}^\infty \int_0^\infty a(n)e^{-e^{nx}}e^{nzx}dx$, for arithmetic functions $a(n)$ and $\Re z>0$

Published on 26 Mar 2026 - 13:01

score 30 · Answer 2 · 2017-02-20 13:33:54

30

Views

asymptotic behavior of a nice summation

Published on 20 Feb 2017 - 13:33

score 321 · Answer 3 · 2017-02-20 19:37:50

321

Views

Sign of integral of $\frac{ 2 ^{\frac{it}{2/3}} \Gamma ( \frac{it +1}{2/3}) }{ 2 ^{\frac{it}{1.5}} \Gamma ( \frac{it +1}{1.5}) } \frac{1}{(a+it)^k}$

Published on 20 Feb 2017 - 19:37

score 359 · Answer 4 · 2026-04-01 12:15:17

359

Views

Is this a better 'natural' extension of factorials than the Gamma function?

Published on 01 Apr 2026 - 12:15

score 509 · Answer 5 · 2017-02-22 13:44:07

509

Views

Convergence of a Series involving Gamma Function

Published on 22 Feb 2017 - 13:44

score 299 · Answer 6 · 2017-02-23 09:09:14

299

Views

differential Gamma function

Published on 23 Feb 2017 - 9:09

score 197 · Answer 7 · 2017-02-23 15:40:16

197

Views

How to estimate this incomplete-Gamma-function-like double integral?

Published on 23 Feb 2017 - 15:40

score 2.8k · Answer 8 · 2017-02-24 07:34:41

2.8k

Views

What is $\Gamma(1/2-n)\Gamma(1/2+n)$?

Published on 24 Feb 2017 - 7:34

score 285 · Answer 9 · 2026-03-25 18:50:15

285

Views

Is there a flaw in the theory of fractional calculus?

Published on 25 Mar 2026 - 18:50

score 164 · Answer 10 · 2017-02-25 22:20:50

164

Views

Simplifying a Gamma over a Gamma

Published on 25 Feb 2017 - 22:20

score 50 · Answer 11 · 2026-03-27 23:35:57

50

Views

Generalization of any product similar to the Gamma function

Published on 27 Mar 2026 - 23:35

score 810 · Answer 12 · 2017-02-27 03:01:08

810

Views

Integer and Complex Values for the Gamma Function:

Published on 27 Feb 2017 - 3:01

score 661 · Answer 13 · 2017-02-27 06:01:36

661

Views

What is $\int_0^\infty\frac{x^{z-1}}{x+1} dx$?

Published on 27 Feb 2017 - 6:01

score 78 · Answer 14 · 2017-02-27 17:16:21

78

Views

How this integral can be calculated?

Published on 27 Feb 2017 - 17:16

score 197 · Answer 15 · 2017-02-27 18:59:18

197

Views

Taking the limit outside the integral

Published on 27 Feb 2017 - 18:59

List Question

On the representation $\Gamma(z)=\sum_{n=2}^\infty \int_0^\infty a(n)e^{-e^{nx}}e^{nzx}dx$, for arithmetic functions $a(n)$ and $\Re z>0$

asymptotic behavior of a nice summation

Sign of integral of $\frac{ 2 ^{\frac{it}{2/3}} \Gamma ( \frac{it +1}{2/3}) }{ 2 ^{\frac{it}{1.5}} \Gamma ( \frac{it +1}{1.5}) } \frac{1}{(a+it)^k}$

Is this a better 'natural' extension of factorials than the Gamma function?

Convergence of a Series involving Gamma Function

differential Gamma function

How to estimate this incomplete-Gamma-function-like double integral?

What is $\Gamma(1/2-n)\Gamma(1/2+n)$?

Is there a flaw in the theory of fractional calculus?

Simplifying a Gamma over a Gamma

Generalization of any product similar to the Gamma function

Integer and Complex Values for the Gamma Function:

What is $\int_0^\infty\frac{x^{z-1}}{x+1} dx$?

How this integral can be calculated?

Taking the limit outside the integral

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