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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
Аннотация:
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.
Ключевые слова:
Hermite–Padé approximants, Jacobi–Piñeiro multiple orthogonal polynomials, functions of the second kind, integral representations, generalized hypergeometric functions.
Поступила в редакцию: 16.08.2019 Исправленный вариант: 30.10.2019 Принята в печать: 29.10.2019
Образец цитирования:
V. G. Lysov, “Integral representations for the Jacobi–Piñeiro polynomials and the functions of the second kind”, Пробл. анал. Issues Anal., 8(26):3 (2019), 83–95
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pa274 https://www.mathnet.ru/rus/pa/v26/i3/p83
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