The Associated Ultraspherical Polynomials and their q -Analogues

Bustoz, Joaquin ; Ismail, Mourad E. H.

Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 718-736

Résumé

A sequence of polynomials {Pn (x)} is orthogonal if Pn (x) is of precise degree n and there is a finite positive measure dμ such that 1.1 A necessary and sufficient condition for orthogonality [9] is that {Pn (x)} satisfies a three term recurrence 1.2 with 1.3 Given a sequence of orthogonal polynomials {Pn (x)} satisfying (1.2), the associated polynomials {Pn (γ)(x)}, γ > 0, are defined by 1.4 with P (γ)-1(x) = 0, P0(γ)(x) = 1, when A n+γ and B n+γ are well-defined.

Détail

DOI : 10.4153/CJM-1982-049-6

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