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Zbl 1171.33304
Lorch, Lee; Muldoon, Martin E.
Monotonic sequences related to zeros of Bessel functions. (English)
[J] Numer. Algorithms 49, No. 1-4, 221-233 (2008). ISSN 1017-1398; ISSN 1572-9265/e

Some inequalities concerning the values of the Bessel functions are proved by A. Akiyama and Y. Tanigawa in the course of their work on Salem numbers and uniform distribution modulo 1. This raises the question of inequalities and monotonicity properties for the sequences of values of one cylinder function at the zeros of another such function. Such results by differential equations methods are derived in this paper.
[Juri M. Rappoport (Moskva)]

MSC 2000:: *33C10 Cylinder functions, etc.
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: Bessel functions; cylinder functions; inequalities; monotonicity properties

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