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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
Gamma functions