This note demonstrates the interlacing property of zeros in Bessel functions, highlighting recurrence relations and curve intersections.
This note presents a simple approach to proving the interlacing properties of positive zeros of Bessel functions of the first kind. The approach relies only on the standard recurrence relations between Bessel functions and characterising intersections between curves, providing a more accessible and intuitive understanding for the interlacing behaviour of the zeros of Bessel functions.
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Dan J. Hill (2025) studied this question.
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