how the gamma functions are used in calculations?

Answer 1

Gamma function is an improper integral.
In some problems where we encounter factorials, to generalize the answer gamma function are used where the number inside the factorial which has to be an integer is replaced by any positive real number.The gamma function is used to interpolate between integer factorials.

You know, its difficult to represent all these on this answer.
so i'm writing gamma funtion as G().

G(n+1)=n!
where n is an integer
also
G(n+1)=(n+1)*G(n)
where n is any non-negative real number.

Answer 2

It is a handy tool for probability things where you want to take the factorial of something that isn't an integer. The gamma function can be used to interpolate between integer factorials.