Two Families of Associated Wilson Polynomials

Ismail, M. E. H. ; Letessier, J. ; Valent, G. ; Wimp, J.

Canadian journal of mathematics, Tome 42 (1990) no. 4, pp. 659-695

Résumé

Two families of associated Wilson polynomials are introduced. Both families are birth and death process polynomials, satisfying the same recurrence relation but having different initial conditions. Contiguous relations for generalized hypergeometric functions of the type 7 F 6 are derived and used to find explicit representations for the polynomials and to compute the corresponding continued fractions. The absolutely continuous components of the orthogonality measures of both families are computed. Generating functions are also given.

Détail

DOI : 10.4153/CJM-1990-035-4

Mots-clés : Wilson polynomials, associated polynomials, generating functions, hypergeometric functions, weight functions, contiguous relations, birth and death processes, 33A65, 42C05

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