Work

Asymptotic Expansions for the Radii of Starlikeness of Normalized q-Bessel Functions

Year: 2024

Type: article

Abstract: In this paper we study the asymptotic behavior of the radii of starlikeness of the normalized Jackson’s second and third q-Bessel functions, focusing on their large orders. To achieve this, we use the Rayleigh sums of positive zeros of both q-Bessel functions, and determine the coefficients of the asymptotic expansions. We derive complete asymptotic expansions for these radii of starlikeness and provide recurrence relations for the coefficients of these expansions. The proofs rely on the notion of Rayleigh sums of positive zeros of q-Bessel functions, Kvitsinsky’s results on spectral zeta functions for q-Bessel functions and asymptotic inversion. Moreover, we derive bounds for the radius of starlikeness of q-Bessel functions by using potential polynomials.

Source: Results in Mathematics

DOI: 10.1007/s00025-024-02277-2

Authors: Árpád Baricz, Pranav Kumar, Sanjeev Singh

Institutions: Obuda University, Babeș-Bolyai University, Indian Institute of Technology Indore

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Óbudai Egyetem, Science and Engineering Research Board