English

The Modified Lommel functions: monotonic pattern and inequalities

Classical Analysis and ODEs 2017-04-18 v1

Abstract

This article studies the monotonicity, log-convexity of the modified Lommel functions by using its power series and infinite product representation. Same properties for the ratio of the modified Lommel functions with the Lommel function, sinh\sinh and cosh\cosh are also discussed. As a consequence, some Tur\'an type and reverse Tur\'an type inequalities are given. A Rayleigh type function for the Lommel functions are derived and as an application, we obtain the Redheffer-type inequality.

Keywords

Cite

@article{arxiv.1704.04667,
  title  = {The Modified Lommel functions: monotonic pattern and inequalities},
  author = {Saiful R Mondal},
  journal= {arXiv preprint arXiv:1704.04667},
  year   = {2017}
}
R2 v1 2026-06-22T19:18:13.407Z