Geodesic
On a Series Representation for Integral Kernels of Transmutation Operators for Perturbed Bessel Equations
Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 552-570.

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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. 
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V. V. Kravchenko; E. L. Shishkina; S. M. Torba. On a Series Representation for Integral Kernels of Transmutation Operators for Perturbed Bessel Equations. Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 552-570. http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a5/

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