Turan Type Inequalities for Tricomi Confluent Hypergeometric Functions

    Authors

    A. Baricz;M. E. H. Ismail

    Comments

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    Abbreviated Journal Title

    Constr. Approx.

    Keywords

    Parabolic cylinder functions; Tricomi confluent hypergeometric; functions; Kummer confluent hypergeometric functions; Whittaker; functions; Modified Bessel functions; Turan type inequalities; Turan; determinants; Logarithmically convex functions; Complete monotonicity; Absolute monotonicity; MODIFIED BESSEL-FUNCTIONS; DENSITY-FUNCTION; MILLS RATIO; MONOTONICITY; DETERMINANTS; PRODUCT; BOUNDS; Mathematics

    Abstract

    Some sharp two-sided Turan type inequalities for parabolic cylinder functions and Tricomi confluent hypergeometric functions are deduced. The proofs are based on integral representations for quotients of parabolic cylinder functions and Tricomi confluent hypergeometric functions, which arise in the study of the infinite divisibility of the Fisher-Snedecor F distribution. Moreover, some complete monotonicity results are given concerning Turan determinants of Tricomi confluent hypergeometric functions. These complement and improve some of the results of Ismail and Laforgia (in Constr. Approx. 26:1-9, 2007).

    Journal Title

    Constructive Approximation

    Volume

    37

    Issue/Number

    2

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    195

    Last Page

    221

    WOS Identifier

    WOS:000314883800002

    ISSN

    0176-4276

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