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Probl. Anal. Issues Anal., 2019, Volume 8(26), Issue 3, Pages 83–95 (Mi pa274)  

Integral representations for the Jacobi–Piñeiro polynomials and the functions of the second kind

V. G. Lysov

Keldysh Institute of Applied Mathemtics, RAS, 4 Miusskaya sq., Moscow 125047, Russia

Abstract: We consider the Hermite–Padé approximants for the Cauchy transforms of the Jacobi weights in one interval. The denominators of the approximants are known as Jacobi–Piñeiro polynomials. These polynomials, together with the functions of the second kind, satisfy a generalized hypergeometric differential equation. In the case of the two weights, we construct the basis of the solutions of this ODE with elements of different growth rate. We obtain the integral representations for the basis elements.

Keywords: Hermite–Padé approximants, Jacobi–Piñeiro multiple orthogonal polynomials, functions of the second kind, integral representations, generalized hypergeometric functions.

DOI: https://doi.org/10.15393/j3.art.2019.6830

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Bibliographic databases:

UDC: 517.53
MSC: 33C20, 33C45
Received: 16.08.2019
Revised: 30.10.2019
Accepted:29.10.2019
Language:

Citation: V. G. Lysov, “Integral representations for the Jacobi–Piñeiro polynomials and the functions of the second kind”, Probl. Anal. Issues Anal., 8(26):3 (2019), 83–95

Citation in format AMSBIB
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\by V.~G.~Lysov
\paper Integral representations for the~Jacobi--Pi\~neiro polynomials and the~functions of the second kind
\jour Probl. Anal. Issues Anal.
\yr 2019
\vol 8(26)
\issue 3
\pages 83--95
\mathnet{http://mi.mathnet.ru/pa274}
\crossref{https://doi.org/10.15393/j3.art.2019.6830}
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\elib{https://elibrary.ru/item.asp?id=41470782}


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