WHAT IS GAMMA FUNCTION AND HOW IT IS USEFUL IN PHYSICS?please explain gamma function.

 Dear arauka

If n is a positive rational number ,then the improper integral

_o∫^∞ e^-x x^n-1 dx  is define as Gamma Function and is denoted by "Γn"

Γn = _o∫^∞ e^-x x^n-1 dx     where x ε Q⁺

this is very special type of intigration you can directlt calculate these type of intigration by using gamma function.

for example you want to calculate

 _o∫^∞ e^-x x³ dx 

then according to gamma function

_o∫^∞ e^-x x³ dx =_o∫^∞ e^-x x^4-1 dx

                         =Γ4=3! =6

where Γ(n+1) =n!

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