Inequalities and Monotonicity Properties for Gamma and q-Gamma Functions

  • Mourad E. H. Ismail
  • Martin E. Muldoon
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 119)


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.


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Copyright information

© Birkhäuser 1994

Authors and Affiliations

  • Mourad E. H. Ismail
    • 1
  • Martin E. Muldoon
    • 2
  1. 1.Department of MathematicsUniversity of South FloridaTampaUSA
  2. 2.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada

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