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Ch 4 - 81E
Chapter 4, Problem 81E(choose chapter or problem)
a If \(\alpha>0\), \(\Gamma(\alpha)\) is defined by \(\Gamma(\alpha)=\int_{0}^{\infty} y^{\alpha-1} e^{-y} d y\), show that .
*b If \(\alpha>1\), integrate by parts to prove that \(\Gamma(\alpha)=(\alpha-1) \Gamma(\alpha-1)\).
Equation Transcription:
Text Transcription:
alpha>0
Gamma(alpha)
Gamma(alpha)=0y-1e-ydy
Gamma(1)=1
alpha>1
Gamma(alpha)=(alpha-1)(alpha-1)
Questions & Answers
QUESTION:
a If \(\alpha>0\), \(\Gamma(\alpha)\) is defined by \(\Gamma(\alpha)=\int_{0}^{\infty} y^{\alpha-1} e^{-y} d y\), show that .
*b If \(\alpha>1\), integrate by parts to prove that \(\Gamma(\alpha)=(\alpha-1) \Gamma(\alpha-1)\).
Equation Transcription:
Text Transcription:
alpha>0
Gamma(alpha)
Gamma(alpha)=0y-1e-ydy
Gamma(1)=1
alpha>1
Gamma(alpha)=(alpha-1)(alpha-1)
ANSWER:
Step 1:Problem
(a)
(b)