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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 8, Pages 1428–1438 (Mi zvmmf11122)  

On one integral equation in the theory of transform operators

S. M. Sitnik

Belgorod State University, Belgorod, 308002 Russia

Abstract: Integral representations of solutions of one differential equation with singularities in the coefficients, containing the Bessel operator perturbed by some potential, are considered. The existence of integral representations of a certain type for such solutions is proved by the method of successive approximations using transform operators. Potentials with strong singularities at the origin are allowed. As compared with the known results, the Riemann function is expressed not via the general hypergeometric function, but, more specifically, via the Legendre function, which helps to avoid unknown constants in the estimates.

Key words: transform operator, Riemann function, Gauss hypergeometric function, Legendre function, singular potential.

DOI: https://doi.org/10.31857/S0044466920080141


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1381–1391

Bibliographic databases:

UDC: 517.926.4
Received: 15.02.2020
Revised: 15.02.2020
Accepted:09.04.2020

Citation: S. M. Sitnik, “On one integral equation in the theory of transform operators”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1428–1438; Comput. Math. Math. Phys., 60:8 (2020), 1381–1391

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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