This article is cited in 16 papers

On a Series Representation for Integral Kernels of Transmutation Operators for Perturbed Bessel Equations

V. V. Kravchenko^ab, E. L. Shishkina^c, S. M. Torba<sup>a

a</sup> CINVESTAV del IPN
^b Southern Federal University
^c Voronezh State University

Abstract: A representation for the kernel of the transmutation operator relating a perturbed Bessel equation to the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure. New properties of the transmutation kernel are established. A new representation of a regular solution of a perturbed Bessel equation is given, which admits a uniform error bound with respect to the spectral parameter for partial sums of the series. A numerical illustration of the application of the obtained result to solve Dirichlet spectral problems is presented.

Keywords: perturbed Bessel equation, transmutation operators, Neumann series of Bessel functions, Erdelyi–Kober operators, Jacobi polynomials, spectral problems.

UDC: 517.912

Received: 06.12.2017

DOI: 10.4213/mzm12150

 English version: Mathematical Notes, 2018, 104:4, 530–544

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