Special linear combinations of orthogonal polynomials

Zinoviy Grinshpun

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


The paper lists a number of problems that motivate consideration of special linear combinations of polynomials, orthogonal with the weight p(x) on the interval (a,b). We study properties of the polynomials, as well as the necessary and sufficient conditions for their orthogonality. The special linear combinations of Chebyshev orthogonal polynomials of four kinds with absolutely constant coefficients hold a distinguished place in the class of such linear combinations.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - 1 Nov 2004


  • Bernstein-Szegö polynomials
  • Chebyshev polynomials
  • Extrema properties
  • Linear combinations
  • Linearization coefficients
  • Orthogonal polynomials
  • Weight function


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