TY - JOUR

T1 - On functions of the second kind in orthogonal polynomial theory

AU - Grinshpun, Edward

AU - Grinshpun, Zinoviy

PY - 2013/5

Y1 - 2013/5

N2 - Agiven weight function p(x) on an interval [a, b] defines uniquely, subject to normalization, a sequence of orthogonal polynomials Pn (x) and their corresponding sequence of functions of the second kind corresponding to them. This paper focuses on the reverse problem of characterizing orthogonal polynomials by means of functions of the second kind, together with the properties of such functions of the second kind. Functions of the second kind for orthogonal polynomials are also of particular interest in that they differ only slightly from the second solution of the differential equation satisfied by the orthogonal polynomials.

AB - Agiven weight function p(x) on an interval [a, b] defines uniquely, subject to normalization, a sequence of orthogonal polynomials Pn (x) and their corresponding sequence of functions of the second kind corresponding to them. This paper focuses on the reverse problem of characterizing orthogonal polynomials by means of functions of the second kind, together with the properties of such functions of the second kind. Functions of the second kind for orthogonal polynomials are also of particular interest in that they differ only slightly from the second solution of the differential equation satisfied by the orthogonal polynomials.

KW - Cauchy integral

KW - Function of the second kind

KW - Orthogonal polynomials

KW - Weight function

UR - http://www.scopus.com/inward/record.url?scp=84878491816&partnerID=8YFLogxK

U2 - 10.1007/s40315-012-0006-7

DO - 10.1007/s40315-012-0006-7

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AN - SCOPUS:84878491816

SN - 1617-9447

VL - 13

SP - 65

EP - 74

JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

IS - 1

ER -