A definition of the gamma function due to Carl Friedrich
Chapter , Problem 7E(choose chapter or problem)
A definition of the gamma function due to Carl Friedrich Gauss that is valid for all real numbers, except x = 0, 1, 2, . . . , is given by
\(\Gamma(x)=\lim _{n \rightarrow} \frac{n ! n^{x}}{x(x+1)(x+2) \cdots(x+n)}\).
Use this definition to show that \(\Gamma(x+1)=x \Gamma(x)\).
Text Transcription:
Gamma x = lim _n rightarrow n n^x x x+1/x+2 cdots(x+n)
Gamma(x+1)=x Gamma x
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