Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T17:20:18.518Z Has data issue: false hasContentIssue false
  • English
  • Français

Connection Coefficients of Orthogonal Polynomials

Published online by Cambridge University Press:  20 November 2018

Ryszard Szwarc
Ryszard Szwarc*
Affiliation:
Institute of Mathematics University of Wroclaw pi. Grunwaldzki 2/4 50-384 Wroclaw Poland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let be polynomials orthogonal with respect to different distributions. Conditions are given which imply that the coefficients in the expansion of Pn in terms of Q0, Q1,..., Qn are non-negative.

Keywords

39A70orthogonal polynomialsrecurrence formula
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 548 - 556
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Askey, R., Orthogonal expansions with positive coefficients, Proc. Amer. Math. Soc. 26(1965), 1191–1194.Google Scholar
2. Askey, R., Orthogonal Polynomials and Special Functions, Regional Conference Series in Applied Mathematics 21, SIAM, Philadelphia, Pensylwania, 1975.Google Scholar
3. Trench, W. F., Nonnegative and alternating expansions of one set of orthogonal polynomials in terms of another, SIAM J. Math. Anal. 4(1973), 111–115.Google Scholar
4. Trench, W. F., Proof of a conjecture of Askey on orthogonal expansions with positive coefficients, Bull. Amer. Math. Soc. 81(1975), 954–955.Google Scholar
5. Szwarc, R., Orthogonal polynomials and a discrete boundary value problem I, SIAM J. Math. Anal. (4) 23(1992).Google Scholar
6. Wilson, M. W., Nonnegative expansions of polynomials, Proc. Amer. Math. Soc. 24(1970), 100–102.Google Scholar