Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-27T11:42:26.404Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Characterizations of the Ultraspherical Polynomials

Published online by Cambridge University Press:  20 November 2018

N.A. Al-Salam  and
W. A. Al-Salam
N.A. Al-Salam
Affiliation:
University of Alberta Edmonton
W. A. Al-Salam
Affiliation:
University of Alberta Edmonton
Rights & Permissions [Opens in a new window]

Extract

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 the nth ultraspherical polynomial. Also let . The following generating relation is well known (3, p.98).

It can also be written as

1.1

This suggests the consideration of the class of polynomial sets {Qn(x), n = 0, 1, 2,…}, Qn(x) is of exact degree n and

1.2

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 3 , August 1968 , pp. 457 - 464
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Danese, A., On a characterization of ultraspherical polynomials, Boll. Unione Mat. Italiana (3) vol 21 (1966) 368-370.Google Scholar
2. Illief, L., Orthogonale systeme in eunigen Klassen von Polynomenfolgen. Comptes Rendus de l'academie bulgare de Sciences, Tome 18, no. 4 (1965) 295-298.Google Scholar
3. Szegö, G., Orthogonal polynomials. (AMS Coll. publ. rev. ed. vol 23, New York, 1959).Google Scholar