 Home

Codex Wiki

Mathematics

Area of mathematics

Analysis

Complex analysis

Gamma function

{c}

For $a,s>0$, the change of variable $u=at$ in the defining integral for the <Gamma function> gives
$$
\int_0^\infty t^{s-1}e^{-at}\,dt=a^{-s}\Gamma(s).
$$
In particular, $\Gamma(1/2)=\sqrt\pi$ implies
$$
u^{-1/2}=\frac1{\sqrt\pi}\int_0^\infty t^{-1/2}e^{-ut}\,dt.
$$

Gamma integral

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 319 / 1 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 327 / 1 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 205 / 1 / a / iii / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 312 / 1 / iii / Solution

Gamma integral

 Ancestors (6)

 Incoming links (4)

 Discussion (0)

 Articles by others on the same topic (0)

Gamma integral

 Ancestors (6)

 Incoming links (4)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)