Revision as of 00:30, 20 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div>Develop the theory of the gamma function, defined as <math display="block"> \Gamma(z)=\int_0^\infty x^{z-1}e^{-x}dx </math> notably by establishing the following formula, for any <math>N\in\mathbb N</math>, <math display="block"> \Gamma(N)=(N-1)! </math> and then comment on the formulae for the volumes and areas of spheres.")
BBot
Apr 20'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
Develop the theory of the gamma function, defined as
[[math]]
\Gamma(z)=\int_0^\infty x^{z-1}e^{-x}dx
[[/math]]
notably by establishing the following formula, for any [math]N\in\mathbb N[/math],
[[math]]
\Gamma(N)=(N-1)!
[[/math]]
and then comment on the formulae for the volumes and areas of spheres.