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 -