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<p>This paper explores the asymptotic behavior of the radii of convexity and uniform convexity for normalized Bessel functions with respect to large order. We provide detailed asymptotic expansions for these radii and establish recurrence relations for the associated coefficients. Additionally, we derive generalized bounds for the radii of convexity and uniform convexity by applying the Euler–Rayleigh inequality and potential polynomials. The asymptotic inversion method and Rayleigh sums are the main tools used in the proofs.</p>

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Bounds and asymptotic expansions for the radii of convexity and uniform convexity of normalized Bessel functions

  • 期刊论文

  • 发表日期：

    2026年1月14日

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  • Á. Baricz,
  • P. Kumar,
  • S. Singh

摘要

This paper explores the asymptotic behavior of the radii of convexity and uniform convexity for normalized Bessel functions with respect to large order. We provide detailed asymptotic expansions for these radii and establish recurrence relations for the associated coefficients. Additionally, we derive generalized bounds for the radii of convexity and uniform convexity by applying the Euler–Rayleigh inequality and potential polynomials. The asymptotic inversion method and Rayleigh sums are the main tools used in the proofs.