Some gamma function inequalities

Author:
Horst Alzer

Journal:
Math. Comp. **60** (1993), 337-346

MSC:
Primary 33B15; Secondary 26D20

DOI:
https://doi.org/10.1090/S0025-5718-1993-1149288-7

MathSciNet review:
1149288

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Abstract | References | Similar Articles | Additional Information

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 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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1993-1149288-7

Keywords:
Gamma function,
psi function,
complete monotonicity,
inequalities,
identric mean,
infinite divisibility,
Laplace transform

Article copyright:
© Copyright 1993
American Mathematical Society