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Monotonicity results for the gamma function. (English) Zbl 0805.33001

This paper proves that \([\Gamma(1+ 1/x)]^ x\) decreases with \(x\), where \(0< x<\infty\), and \(x[\Gamma(1+ 1/x)]^ x\) increases with \(x\), where \(0< x<\infty\).

MSC:

33B15 Gamma, beta and polygamma functions

Keywords:

Gamma functions
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