Numerical Algorithms

, Volume 49, Issue 1, pp 221–233

Monotonic sequences related to zeros of Bessel functions

Authors

  • Lee Lorch
    • Department of Mathematics & StatisticsYork University
    • Department of Mathematics & StatisticsYork University
Original Paper

DOI: 10.1007/s11075-008-9189-4

Cite this article as:
Lorch, L. & Muldoon, M.E. Numer Algor (2008) 49: 221. doi:10.1007/s11075-008-9189-4

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 functionsCylinder functionsInequalitiesMonotonicity properties

Mathematics Subject Classifications (2000)

Primary 33C10Secondary 34C10

Copyright information

© Springer Science+Business Media, LLC. 2008