Author:
Elbert Árpád,Siafarikas Panayiotis D.
Abstract
AbstractLet Jv,1 be the smallest (first) positive zero of the Bessel function Jv(z), v > −1, which becomes zero when v approaches −1. Then can be continued analytically to −2 < v < −1, where it takes on negative values. We show that is a convex function of v in the interval −2 < v ≤ 0, as an addition to an old result [Á. Elbert and A. Laforgia, SIAM J. Math. Anal. 15(1984), 206–212], stating this convexity for v > 0. Also the monotonicity properties of the functions are determined. Our approach is based on the series expansion of Bessel function Jv(z) and it turned out to be effective, especially when −2 < v < −1.
Publisher
Canadian Mathematical Society
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献