Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - October 2010 - Volume 53, Issue 03  

Research Article

Bounds for modified Bessel functions of the first and second kinds

Árpád Baricza1

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

Abstract

Some new inequalities for quotients of modified Bessel functions of the first and second kinds are deduced. Moreover, some developments on bounds for modified Bessel functions of the first and second kinds, higher-order monotonicity properties of these functions and applications to a special function that arises in finite elasticity, are summarized. The key tool in our proofs is a frequently used criterion for the monotonicity of the quotient of two Maclaurin series.

(Received October 09 2008)

Key Words

  • modified Bessel functions;
  • complete monotonicity;
  • absolute monotonicity;
  • bounds

2010 Mathematics subject classification

  • Primary 33C10;
  • 33C15

Footnotes

Dedicated to my daughter, Boróka