Mourad E. H. Ismail, Martin E. Muldoon
Published 2013-01-09Version 1
We prove some new results and unify the proofs of old ones involving complete monotonicity of expressions involving gamma and $q$-gamma functions, $0 < q < 1$. Each of these results implies the infinite divisibility of a related probability measure. In a few cases, we are able to get simple monotonicity without having complete monotonicity. All of the results lead to inequalities for these functions. Many of these were motivated by the bounds in a 1959 paper by Walter Gautschi. We show that some of the bounds can be extended to complex arguments.
Comments: 16 pages; corrected version of paper published in 1994
Journal: Approximation and Computation: A Festschrift in Honor of Walter Gautschi, ISNM, vol. 119 (1994) pp. 309-323
Some inequalities for the $q$-Extension of the Gamma Function
Inequalities for series in q-shifted factorials and q-gamma functions
Complete monotonicity of a function involving the $p$-psi function and alternative proofs
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