Complex zeros of Bessel function derivatives and associated orthogonal polynomials

2024/06/14 by Seok-Young Chung, Sujin Lee, Chung, Seok-Young +3
Mathematics · #30B70 #30C15 #33C10 #33C47 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical Inequalities and Applications #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2406.09746

openalex publication_date 2024/06/14 · openalex created_date 2024/06/18 · openalex updated_date 2026/07/28

Abstract

We introduce a sequence of orthogonal polynomials whose associated moments are the Rayleigh-type sums, involving the zeros of the Bessel derivative J_ν' of order ν. We also discuss the fundamental properties of those polynomials such as recurrence, orthogonality, etc. Consequently, we obtain a formula for the Hankel determinant, elements of which are chosen as the aforementioned Rayleigh-type sums. As an application, we complete the Hurwitz-type theorem for J_ν', which deals with the number of complex zeros of J_ν' depending on the range of ν.

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