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Bounds for modified Bessel functions of the first and second kinds

Published online by Cambridge University Press:  05 August 2010

Árpád Baricz
Árpád Baricz
Affiliation:
Department of Economics, Babeş-Bolyai University, Cluj-Napoca 400591, Romania, ([email protected])
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Abstract

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Some new inequalities for quotients of modified Bessel functions of the first and second kinds are deduced. Moreover, some developments on bounds for modified Bessel functions of the first and second kinds, higher-order monotonicity properties of these functions and applications to a special function that arises in finite elasticity, are summarized. The key tool in our proofs is a frequently used criterion for the monotonicity of the quotient of two Maclaurin series.

Keywords

modified Bessel functionscomplete monotonicityabsolute monotonicitybounds

MSC classification

Secondary: 33C10: Bessel and Airy functions, cylinder functions, $_0F_1$ 33C15: Confluent hypergeometric functions, Whittaker functions, $_1F_1$
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 3 , October 2010 , pp. 575 - 599
Copyright
Copyright © Edinburgh Mathematical Society 2010

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