Answer: The Gamma Function The Gamma Function is defined by (a) Find and (b) Use

Chapter 8, Problem 103

(choose chapter or problem)

The Gamma Function The Gamma Function \(\Gamma(n)\) is defined by

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

(a) Find \(\Gamma(1), \Gamma(2), \text { and } \Gamma(3)\).

(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)

Gamma(1), Gamma(2) and Gamma(3)

Gamma(n+1)n Gamma(n)