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arXiv · 2310.13542

On the generalized interlacing property for the zeros of Bessel functions

Seok-Young Chung·Sujin Lee·Young Woong Park
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Abstract

This paper investigates a generalized interlacing property between Bessel functions, particularly $J_\nu$ and $J_\mu$, where the difference $|\nu-\mu|$ exceeds $2$. This interlacing phenomenon is marked by a compensatory interaction with the zeros of Lommel polynomials, extending our understanding beyond the traditional $|\nu-\mu| \le 2$ regime. The paper extends the generalized interlacing property to cylinder functions and derivative of Bessel functions, as an application. It is also discussed that Siegel's extension of Bourget hypothesis to rational numbers of $\nu$ cannot be further improved to arbitrary real numbers.

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Seok-Young Chung, Sujin Lee, Young Woong Park. 2023-10-20. On the generalized interlacing property for the zeros of Bessel functions. https://doi.org/10.1016/j.jmaa.2024.128495

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