K. B. Sabitov, “On the uniform convergence of the expansion of a function in Fourier–Bessel range”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, Number 11,Pages <nobr>89

This article is cited in 5 papers

On the uniform convergence of the expansion of a function in Fourier–Bessel range

K. B. Sabitov^ab

^a Institute of Mathematics with Computing Centre Ufa Federal Research Centre of the Russian Academy of Sciences, 112 Chernyshevsky str., Ufa, 450008 Russia
^b Sterlitamak branch of the Ufa University of Science and Technology, 49 Lenina Ave., Sterlitamak, 453103 Russia

Abstract: Watson's monograph on the theory of Bessel functions noted the unsolved problem of expanding a function in a Fourier–Bessel series when the order of these functions changes from minus one to minus one second. In this paper, we propose sufficient conditions with respect to the function for which the uniform convergence of the Fourier–Bessel series to a given function for the indicated index values.

Keywords: Fourier–Bessel series, uniform convergence, sufficient conditions.

UDC: 517.52

Received: 11.01.2022
Revised: 22.03.2022
Accepted: 08.04.2022

DOI: 10.26907/0021-3446-2022-11-89-96