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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
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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