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