Bounds and inequalities of the modified Lommel functions
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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\'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.
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\'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.
참고문헌 (19)
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