A note on zeros of derivatives of ultraspherical Bessel functions

2025/08/22 by Jiang, Tao · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.16426

Abstract

For any fixed ν≥ 0, δ∈ \mathbb R and x>0, we investigate the positive zeros of the derivatives j'_ν,δ(x) and y'_ν,δ(x), where j_ν,δ(x)=x^-δJ_ν(x)\quadand y_ν,δ(x)=x^-δY_ν(x). We derive asymptotic expansions for their k-th positive zeros as k→ ∞.

Citations

• Bessel functions and Weyl's law for balls and spherical shells
• Uniform enclosures for the phase and zeros of Bessel functions and their derivatives
• A note on the Weyl formula for balls in ℝ^d
• The Weyl formula for planar annuli

Cited by

• Pólya's conjecture for higher-dimensional Neumann balls

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