On functions of the second kind in orthogonal polynomial theory

Edward Grinshpun; Zinoviy Grinshpun

doi:10.1007/s40315-012-0006-7

On functions of the second kind in orthogonal polynomial theory

Edward Grinshpun
, Zinoviy Grinshpun

Department of Mathematics

Lucent

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Agiven weight function p(x) on an interval [a, b] defines uniquely, subject to normalization, a sequence of orthogonal polynomials P_n (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.

Original language	English
Pages (from-to)	65-74
Number of pages	10
Journal	Computational Methods and Function Theory
Volume	13
Issue number	1
DOIs	https://doi.org/10.1007/s40315-012-0006-7
State	Published - May 2013

Keywords

Cauchy integral
Function of the second kind
Orthogonal polynomials
Weight function

Access to Document

10.1007/s40315-012-0006-7

Cite this

@article{cdb5d94155804f7d98a6a191d12884a4,

title = "On functions of the second kind in orthogonal polynomial theory",

abstract = "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.",

keywords = "Cauchy integral, Function of the second kind, Orthogonal polynomials, Weight function",

author = "Edward Grinshpun and Zinoviy Grinshpun",

year = "2013",

month = may,

doi = "10.1007/s40315-012-0006-7",

language = "אנגלית",

volume = "13",

pages = "65--74",

journal = "Computational Methods and Function Theory",

issn = "1617-9447",

publisher = "Springer Science and Business Media Deutschland GmbH",

number = "1",

}

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 - https://www.scopus.com/pages/publications/84878491816

U2 - 10.1007/s40315-012-0006-7

DO - 10.1007/s40315-012-0006-7

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

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 -

On functions of the second kind in orthogonal polynomial theory

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this