Title

Turán Type Inequalities For Tricomi Confluent Hypergeometric Functions

Keywords

Absolute monotonicity; Complete monotonicity; Kummer confluent hypergeometric functions; Logarithmically convex functions; Modified Bessel functions; Parabolic cylinder functions; Tricomi confluent hypergeometric functions; Turán determinants; Turán type inequalities; Whittaker functions

Abstract

Some sharp two-sided Turán 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 Turán 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). © 2012 Springer Science+Business Media, LLC.

Publication Date

4-1-2013

Publication Title

Constructive Approximation

Volume

37

Issue

2

Number of Pages

195-221

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00365-012-9171-1

Socpus ID

84874011423 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84874011423

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