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.
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To the memory of Luigi Gatteschi.
This work was supported by grants from the Natural Sciences and Engineering Research Council, Canada.
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Lorch, L., Muldoon, M.E. Monotonic sequences related to zeros of Bessel functions. Numer Algor 49, 221–233 (2008). https://doi.org/10.1007/s11075-008-9189-4
- Bessel functions
- Cylinder functions
- Monotonicity properties
Mathematics Subject Classifications (2000)
- Primary 33C10
- Secondary 34C10