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http://dx.doi.org/10.4134/CKMS.c180205

BOUNDS AND INEQUALITIES OF THE MODIFIED LOMMEL FUNCTIONS  

Mondal, Saiful R. (Department of Mathematics and Statistics Collage of Science King Faisal University)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.2, 2019 , pp. 573-583 More about this Journal
Abstract
This article studies the monotonicity, log-convexity of the modified Lommel functions by using its power series and infinite product representation. Some properties for the ratio of the modified Lommel functions with the Lommel function, sinh and cosh are also discussed. As a consequence, $Tur{\acute{a}}n$ type and reverse $Tur{\acute{a}}n$ 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
Lommel functions; modified Lommel functions; $Tur{\acute{a}}n$-type inequality; monotonicity properties; log-convexity;
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