Turán Type Inequalities for Tricomi Confluent Hypergeometric Functions

Árpád Baricz, Mourad E.H. Ismail

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15 Citations (Scopus)

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).

Original languageEnglish
Pages (from-to)195-221
Number of pages27
JournalConstructive Approximation
Volume37
Issue number2
DOIs
Publication statusPublished - Feb 22 2013

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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

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Computational Mathematics

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