# Gamma Function

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 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    Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

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