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Special functions, infinite divisibility and transcendental equations

Published online by Cambridge University Press:  24 October 2008

Mourad E. H. Ismail  and
C. Ping May
Mourad E. H. Ismail
Affiliation:
McMaster University, Hamilton, Ontario, Canada
C. Ping May
Affiliation:
University of Alberta, Edmonton, Alberta, Canada
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Abstract

We establish integral representations for quotients of Tricomi ψ functions and of several quotients of modified Bessel functions and of linear combinations of them. These integral representations are used to prove the complete monotonicity of the functions considered and to prove the infinite divisibility of a three parameter probability distribution. Limiting cases of this distribution are the hitting time distributions considered recently by Kent and Wendel. We also derive explicit formulas for the Kent–Wendel probability density functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 3 , May 1979 , pp. 453 - 464
Copyright
Copyright © Cambridge Philosophical Society 1979

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