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. 
@article{MZM_2018_104_4_a5,
     author = {V. V. Kravchenko and E. L. Shishkina and S. M. Torba},
     title = {On a {Series} {Representation} for {Integral} {Kernels} of {Transmutation} {Operators} for {Perturbed} {Bessel} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {552--570},
     publisher = {mathdoc},
     volume = {104},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a5/}
}
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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/