Numerical Algorithms

, Volume 49, Issue 1–4, pp 221–233 | Cite as

Monotonic sequences related to zeros of Bessel functions

Original Paper

Abstract

In the course of their work on Salem numbers and uniform distribution modulo 1, A. Akiyama and Y. Tanigawa proved some inequalities concerning the values of the Bessel function J0 at multiples of π, i.e., at the zeros of J1/2. 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. Here we derive such results by differential equations methods.

Keywords

Bessel functions Cylinder functions Inequalities Monotonicity properties 

Mathematics Subject Classifications (2000)

Primary 33C10 Secondary 34C10 

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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsYork UniversityTorontoCanada

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