The Modified Lommel functions: monotonic pattern and inequalities

2017/04/15 by Saiful R. Mondal, Mondal, Saiful R
Mathematics · #33C10 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1704.04667

openalex publication_date 2017/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 and \cosh are also discussed. As a consequence, some Turán type and reverse Turán type inequalities are given. A Rayleigh type function for the Lommel functions are derived and as an application, we obtain the Redheffer-type inequality.

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