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

共 50 条

[31] A Jacobi Spectral Method for Solving Multidimensional Linear Volterra Integral Equation of the Second Kind
Yunxia Wei
Yanping Chen
Journal of Scientific Computing, 2019, 79 : 1801 - 1813
[32] Using Chebyshev's polynomials for solving Fredholm integral equations of the second kind
Ezquerro, Jose Antonio
Hernandez-Veron, Miguel Agel
MATHEMATICAL MODELLING AND ANALYSIS, 2025, 30 (01) : 36 - 51
[33] A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel
Guo, Hongfeng
Cai, Haotao
Zhang, Xin
ABSTRACT AND APPLIED ANALYSIS, 2014,
[34] A note on the Gauss-Jacobi quadrature formulae for singular integral equations of the second kind
Lifeng Ma
Alexander M. Korsunsky
International Journal of Fracture, 2004, 126 : 399 - 405
[35] Shapiro Polynomials of the Second Kind
Stojanoska, I. S.
VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS, 2013, 46 (04) : 175 - 179
[36] INTEGRAL REPRESENTATIONS FOR SPECTRAL FUNCTIONS OF SOME NONSELF-ADJOINT JACOBI MATRICES
Zagorodnyuk, S. M.
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2009, 15 (01): : 91 - 100
[37] Integral and series representations of q-polynomials and functions: Part I
Ismail, Mourad E. H.
Zhang, Ruiming
ANALYSIS AND APPLICATIONS, 2018, 16 (02) : 209 - 281
[38] Some Identities on the Second Kind Bernoulli Polynomials of order α and Second Kind Euler Polynomials of order α
Kurt, Burak
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B, 2012, 1479 : 352 - 355
[39] Representations of integral quadratic polynomials
Chan, Wai Kiu
Oh, Byeong-Kweon
DIOPHANTINE METHODS, LATTICES, AND ARITHMETIC THEORY OF QUADRATIC FORMS, 2013, 587 : 31 - +
[40] INTEGRAL REPRESENTATIONS FOR ULTRASPHERICAL POLYNOMIALS
BINGHAM, NH
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1972, 6 (DEC): : 1 - 11

← 1 2 3 4 5 →