# Gamma Function

• Difficulty Level : Medium
• Last Updated : 16 Jun, 2020

Gamma function is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers.

Gamma function denoted by is defined as: where p>0.
Gamma function is also known as Euler’s integral of second kind.
Integrating Gamma function by parts we get,   Thus Attention reader! Don’t stop learning now. Get hold of all the important CS Theory concepts for SDE interviews with the CS Theory Course at a student-friendly price and become industry ready.

Some standard results:

1. We know that Put t=u^2
Thus   Now changing to polar coordinates by using u = r cosθ and v = r sinθ
Thus   Hence 2. Where n is a positive integer and m>-1
Put x=e^-y such that dx=-e-ydy=-x dy  Put (m+1)y = u  Example-1:
Compute Explanation :
Using     We know Thus Example-2:
Evaluate Explanation :
Put x4 = t, 4x3dx = dt, dx = ¼ t-3/4 dt    My Personal Notes arrow_drop_up