## 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