The Gamma Function is defined by (a) Find and (b) Use integration by parts to show that

Chapter 8, Problem 101

(choose chapter or problem)

The Gamma Function The Gamma Function is defined by

\(\Gamma(n)=\int_{0}^{\infty} x^{n-1} e^{-x} d x, \quad n>0\)

(a) Find \(\Gamma(1)\), \(\Gamma(2)\), and \(\Gamma(3)\)

(b) Use integration by parts to show that \(\Gamma(n+1)=n \Gamma(n)\).

(c) Write \(\Gamma(n)\) using factorial notation where n is a positive integer. 

Text Transcription:

Gamma(n)=int_0^infty x^n-1 e^-x dx, quad n>0

Gamma(1)

Gamma(2)

Gamma(3)

Gamma(n+1)=n \Gamma(n)

Gamma(n)

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