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 nonpositive 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:

We know that
Put t=u^2
Thus
Now changing to polar coordinates by using u = r cosθ and v = r sinθ
Thus
Hence 
Where n is a positive integer and m>1
Put x=e^y such that dx=e^{y}dy=x dy
Put (m+1)y = u
Example1:
Compute
Explanation :
Using
We know
Thus
Example2:
Evaluate
Explanation :
Put x^{4} = t, 4x^{3}dx = dt, dx = ¼ t^{3/4} dt
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