Question

Evaluate $\int_{0}^{\infty}e^{-x^2}\ln(x)dx$

score 126 · Answer 1 · 2026-03-25 19:01:07

126

Views

Evaluate $\int_{0}^{\infty}e^{-x^2}\ln(x)dx$

Published on 25 Mar 2026 - 19:01

score 240 · Answer 2 · 2026-04-07 18:44:20

240

Views

Inversion of Gamma and Zeta Functions through Fourier Transform

Published on 07 Apr 2026 - 18:44

score 113 · Answer 3 · 2017-11-30 13:19:41

113

Views

Is $\lim_{n\to\infty}2^{-n/2}\sum_{k=1}^{n-1}\frac{k^2\cdot2^{k/2}}{k+\frac{1}{2}}\left(\frac{\Gamma(k)}{\Gamma(k+\frac{1}{2})}\right)^2=1+\sqrt{2}$?

Published on 30 Nov 2017 - 13:19

score 206 · Answer 4 · 2017-11-30 16:55:16

206

Views

Show that $\int_{\mu}^{\infty} \frac{1}{\Gamma(k)} z^{k-1} e^{-z}dz = \sum_{x = 0}^{k-1} \frac{\mu^x}{x!e^\mu}$.

Published on 30 Nov 2017 - 16:55

score 2.5k · Answer 5 · 2017-12-02 19:15:56

2.5k

Views

Incomplete Gamma function of negative arguments

Published on 02 Dec 2017 - 19:15

score 168 · Answer 6 · 2017-12-04 03:46:47

168

Views

How to integrate this integral $\int _{0}^{1} \frac{dx}{\sqrt{x(x^2-1)}}$??

Published on 04 Dec 2017 - 3:46

score 145 · Answer 7 · 2017-12-04 22:13:51

145

Views

What happens to $\sin(\frac{\pi s}{2})\Gamma(1-s)$ at $s=2,4,6,...$

Published on 04 Dec 2017 - 22:13

score 150 · Answer 8 · 2017-12-06 12:14:57

150

Views

Evaluate $\int_0^a \sqrt{\frac{x^3}{a^3-x^3}} dx$.

Published on 06 Dec 2017 - 12:14

score 410 · Answer 9 · 2026-04-01 09:31:36

410

Views

Approximate variance of sample standard deviation based on the Gamma function

Published on 01 Apr 2026 - 9:31

score 414 · Answer 10 · 2017-12-15 21:20:17

414

Views

The proof of Holder's theorem for Gamma function(transcendentally transcendental)

Published on 15 Dec 2017 - 21:20

score 768 · Answer 11 · 2017-12-16 04:38:53

768

Views

Gamma reflection formula proof

Published on 16 Dec 2017 - 4:38

score 181 · Answer 12 · 2017-12-16 10:23:09

181

Views

Series of Gamma functions involving $\Gamma \left(\frac{n}{2} (1-i x)\right) \Gamma \left(\frac{n}{2} (1+i x)\right)$?

Published on 16 Dec 2017 - 10:23

score 447 · Answer 13 · 2026-03-27 23:23:17

447

Views

Showing the relationship between $B$ and $\Gamma$ without multivariate calculus

Published on 27 Mar 2026 - 23:23

score 64 · Answer 14 · 2026-04-05 18:39:25

64

Views

Calculate $(-1)^k \left(\begin{matrix} -1/2 \\ k\end{matrix}\right)$. Is it equal to $\frac {(2k)!}{2^{2k}(k!)^2}$?

Published on 05 Apr 2026 - 18:39

score 579 · Answer 15 · 2026-04-02 13:23:57

579

Views

Relationship between integral of a function and integral of square of function

Published on 02 Apr 2026 - 13:23

List Question

Evaluate $\int_{0}^{\infty}e^{-x^2}\ln(x)dx$

Inversion of Gamma and Zeta Functions through Fourier Transform

Is $\lim_{n\to\infty}2^{-n/2}\sum_{k=1}^{n-1}\frac{k^2\cdot2^{k/2}}{k+\frac{1}{2}}\left(\frac{\Gamma(k)}{\Gamma(k+\frac{1}{2})}\right)^2=1+\sqrt{2}$?

Show that $\int_{\mu}^{\infty} \frac{1}{\Gamma(k)} z^{k-1} e^{-z}dz = \sum_{x = 0}^{k-1} \frac{\mu^x}{x!e^\mu}$.

Incomplete Gamma function of negative arguments

How to integrate this integral $\int _{0}^{1} \frac{dx}{\sqrt{x(x^2-1)}}$??

What happens to $\sin(\frac{\pi s}{2})\Gamma(1-s)$ at $s=2,4,6,...$

Evaluate $\int_0^a \sqrt{\frac{x^3}{a^3-x^3}} dx$.

Approximate variance of sample standard deviation based on the Gamma function

The proof of Holder's theorem for Gamma function(transcendentally transcendental)

Gamma reflection formula proof

Series of Gamma functions involving $\Gamma \left(\frac{n}{2} (1-i x)\right) \Gamma \left(\frac{n}{2} (1+i x)\right)$?

Showing the relationship between $B$ and $\Gamma$ without multivariate calculus

Calculate $(-1)^k \left(\begin{matrix} -1/2 \\ k\end{matrix}\right)$. Is it equal to $\frac {(2k)!}{2^{2k}(k!)^2}$?

Relationship between integral of a function and integral of square of function

Trending Questions

Popular # Hahtags

Popular Questions