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arXiv · 1405.4712

Modified Dini functions: monotonicity patterns and functional inequalities

Á. Baricz·S. Ponnusamy·S. Singh
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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 introducing 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, which was very useful in determining the radius of convexity of some normalized Bessel functions of the first kind.

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Á. Baricz, S. Ponnusamy, S. Singh. 2014-05-19. Modified Dini functions: monotonicity patterns and functional inequalities. https://doi.org/10.1007/s10474-016-0599-9

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