INTEGRAL REPRESENTATIONS FOR THE JACOBI - PINEIRO POLYNOMIALS AND THE FUNCTIONS OF THE SECOND KIND

被引：0

作者：

Lysov, V. G. ^{[1
]}

机构：

[1] RAS, Keldysh Inst Appl Math, 4 Miusskaya Sq, Moscow 125047, Russia

来源：

PROBLEMY ANALIZA-ISSUES OF ANALYSIS | 2019年 / 8卷 / 03期

关键词：

Hermite - Pade approximants; Jacobi - Pineiro multiple orthogonal polynomials; functions of the second kind; integral representations; generalized hypergeometric functions; MULTIPLE ORTHOGONAL POLYNOMIALS;

D O I：

10.15393/j3.art.2019.6830

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Hermite - Pade approximants for the Cauchy transforms of the Jacobi weights in one interval. The denominators of the approximants are known as Jacobi - Pineiro 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.

引用

页码：83 / 95

页数：13

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