Original Paper

Numerical Algorithms

, Volume 49, Issue 1, pp 221-233

First online:

Monotonic sequences related to zeros of Bessel functions

  • Lee LorchAffiliated withDepartment of Mathematics & Statistics, York University
  • , Martin E. MuldoonAffiliated withDepartment of Mathematics & Statistics, York University Email author 

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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 J 0 at multiples of π, i.e., at the zeros of J 1/2. 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.


Bessel functions Cylinder functions Inequalities Monotonicity properties

Mathematics Subject Classifications (2000)

Primary 33C10 Secondary 34C10