Bulletin of the Australian Mathematical Society

Research Article

TURÁN TYPE INEQUALITIES FOR MODIFIED BESSEL FUNCTIONS

ÁRPÁD BARICZa1

a1 Department of Economics, Babeş-Bolyai University, Cluj-Napoca 400591, Romania (email: bariczocsi@yahoo.com)

Abstract

In this paper our aim is to deduce some sharp Turán type inequalities for modified Bessel functions of the first and second kinds. Our proofs are based on explicit formulas for the Turánians of the modified Bessel functions of the first and second kinds and on a formula which is related to the infinite divisibility of the Student t-distribution.

(Received December 05 2009)

2000 Mathematics subject classification

  • primary 33C10; secondary 39B62

Keywords and phrases

  • modified Bessel functions;
  • Bessel functions;
  • Turán type inequalities

Footnotes

Research supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

Dedicated to my daughter Boróka