Cross-product of Bessel functions: Monotonicity patterns and functional inequalities

Proceedings of the Indian Academy of Sciences. Mathematical sciences

SAMINATHAN PONNUSAMY^3¹  SANJEEV SINGH^4²  ÁRPÁD BARICZ^1,2⁴ 

[1] Department of Economics, Babe¸s-Bolyai University, Cluj-Napoca 400591, Romania^2;Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India^3;Discipline of Mathematics, Indian Institute of Technology Indore, Indore 453 552, India^4;Institute of Applied Mathematics, Óbuda University, Budapest 1034, Hungary^1

关键词: Functional inequalities;    Bessel functions;    cross-product of Bessel functions;    interlacing of zeros of Bessel and related functions;    Redheffer-type inequalities;    infinite product representation;    absolutely monotonic and log-concave functions;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, we study the Dini functions and the cross-product of Bessel functions. Moreover, we are interested on the monotonicity patterns for the cross-product of Bessel and modified Bessel functions. In addition, we deduce Redheffer-type inequalities, and the interlacing property of the zeros of Dini functions and the cross-product of Bessel and modified Bessel functions. Bounds for logarithmic derivatives ofthese functions are also derived. The key tools in our proofs are some recently developed infinite product representations for Dini functions and cross-product of Bessel functions.

【 授权许可】

CC BY