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BOUNDS AND INEQUALITIES OF THE MODIFIED LOMMEL FUNCTIONS

  • Mondal, Saiful R. (Department of Mathematics and Statistics Collage of Science King Faisal University)
  • Received : 2018.05.11
  • Accepted : 2018.07.24
  • Published : 2019.04.30
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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.

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References

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