J Austral Math Soc Ser A 50 pp333--342, 1991.

Some Inequalities of Bessel and Modified Bessel Functions

C. M. Joshi and S. K. Bissu

Abstract

Two-sided inequalities for the ratio of modified Bessel functions of first kind are given, which provide sharper upper and lower bounds than has been known earlier. Wronskian type inequalities for Bessel functions are proved, and in the sequel alternative proofs of Turan-type inequalities for Bessel and modified Bessel functions are also discussed. These then lead to a two-sided inequality for Bessel functions. Also incorporated in the discussion is an inequality for the ratio of two Bessel functions for 0 < x < 1. Verifications of these inequalities are pointed out numerically.

1980 AMS Subject Classification (1985 Revision): primary 33A40; secondary 26D99

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Authors

C. M. Joshi

S. K. Bissu

Sukhadia University, Udaipur 313001, India.