Modified Dini functions: monotonicity patterns and functional inequalities

Article Type

Research Article

Publication Title

Acta Mathematica Hungarica

Abstract

We deduce some new functional inequalities, like Turán type inequalities, Redheffer type inequalities, and a Mittag-Leffler expansion for a special combination of modified Bessel functions of the first kind, called modified Dini functions. Moreover, we show the complete monotonicity of a quotient of modified Dini functions by involving a new continuous infinitely divisible probability distribution. The key tool in our proofs is a recently developed infinite product representation for a special combination of Bessel functions of the first kind, which was very useful in determining the radius of convexity of some normalized Bessel functions of the first kind.

First Page

120

Last Page

142

DOI

10.1007/s10474-016-0599-9

Publication Date

6-1-2016

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