Nonnegative linearization and quadratic transformation of Askey-Wilson polynomials

Canadian Mathematical Bulletin

Volumn 39, Issue 2, 1996, Pages 241-249

  Szwarc, Ryszard ^a  

^a UNIVERSITY OF WROC AW   (Poland)

Author keywords

Askey Wilson polynomials; Nonnegative linearization; Orthogonal polynomials

Indexed keywords

EID: 0030167147     PISSN: 00084395     EISSN: None     Source Type: Journal    
DOI: 10.4153/CMB-1996-031-x     Document Type: Article

References (12)

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2. _, Orthogonal polynomials and special functions, Regional Conference Series in Applied Mathematics 21, Society for Industrial and Applied Mathematics, Philadelphia, Pensylwania, 1975.
3. R. Askey and J. A. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54(1985).
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5. G. Gasper, Linearization of the product of Jacobi polynomials, I, Canad. J. Math. 22(1970), 171-175.
6. _, Linearization of the product of Jacobi polynomials. II, ibid., 22(1970), 582-593.
7. _, A convolution structure and positivity of a generalized translation operator for the continuous q-Jacobi polynomials, in Conference on Harmonic Analysis in Honor of Antoni Zygmund, Wadsworth International Group, Belmont, Calif. (1983), 44-59.
8. G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge 35(1990).
9. T. Koornwinder, Discrete hypergroups associated with compact quantum Gelfand pairs, in Applications of Hypergroups and Related Measures Algebras, (eds. W. Connett, M. O. Gebuhrer and A. L. Schwartz), Contemporary Mathematics.
10. M. Rahman, The linearization of the product of continuous q-Jacobi polynomials, Can. J. Math. 33(1981), 961-987.
11. R. Szwarc, Orthogonal polynomials and a discrete boundary value problem, I, II, SIAM J. Math. Anal. 23(1992), 959-964, 965-969.
12. R. Szwarc, Nonnegative linearization and q-ultraspherical polynomials, Methods Appl. Anal., to appear.