The Associated Ultraspherical Polynomials and their q-Analogues
- 1 June 1982
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 34 (3) , 718-736
- https://doi.org/10.4153/cjm-1982-049-6
Abstract
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 An+γ and Bn+γ are well-defined.Keywords
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