On functions of the second kind in orthogonal polynomial theory

Edward Grinshpun, Zinoviy Grinshpun

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)65-74
Number of pages10
JournalComputational Methods and Function Theory
Issue number1
StatePublished - May 2013


  • Cauchy integral
  • Function of the second kind
  • Orthogonal polynomials
  • Weight function


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