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A Note on Completely and Absolutely Monotone Functions

Published online by Cambridge University Press:  20 November 2018

Arvind Mahajan  and
Dieter K. Ross
Arvind Mahajan
Affiliation:
Department of Applied Mathematics La Trobe University, Bundoora, 3083, Australia
Dieter K. Ross
Affiliation:
Department of Applied Mathematics La Trobe University, Bundoora, 3083, Australia
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Abstract

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The solutions of a certain class of first order linear differential equations are shown to be either completely or absolutely monotone depending on the nature of its coefficients. This is a simple theorem which is used to deduce a number of new and interesting results dealing with the complete and absolute monotonicity of functions. In particular, a partial answer is supplied to a question posed by Askey and Pollard: “When is completely monotone?”

Keywords

26D1534A1033A1533A40Completely monotoneabsolutely monotoneInequalitiesBessel functionsgamma functions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 2 , 01 June 1982 , pp. 143 - 148
Copyright
Copyright © Canadian Mathematical Society 1982

References

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