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Mathematics of Computation

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Some gamma function inequalities

Author: Horst Alzer
Journal: Math. Comp. 60 (1993), 337-346
MSC: Primary 33B15; Secondary 26D20
MathSciNet review: 1149288
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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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Keywords: Gamma function, psi function, complete monotonicity, inequalities, identric mean, infinite divisibility, Laplace transform
Article copyright: © Copyright 1993 American Mathematical Society