Some gamma function inequalities

Alzer, Horst

doi:10.1090/S0025-5718-1993-1149288-7

Some gamma function inequalities
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Math. Comp. 60 (1993), 337-346 Request permission

Abstract:

A class of completely monotonic functions are presented involving the gamma function as well as the derivative of the psi function. As a consequence, new upper and lower bounds for the ratio $\Gamma (x + 1)/\Gamma (x + s)$ are obtained and compared with related bounds given in part by J. D. Kečkić and P. M. Vasić. Our results are further applied to obtain functions which are Laplace transforms of infinitely divisible probability measures.

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