Modified Dini functions: monotonicity patterns and functional inequalities

Baricz, Árpád and Ponnusamy, Saminathan and Singh, Sanjeev (2016) Modified Dini functions: monotonicity patterns and functional inequalities. ACTA MATHEMATICA HUNGARICA, 149 (1). pp. 120-142. ISSN 0236-5294

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Abstract

We deduce some new functional inequalities, like Turan 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.

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