Vol. 104, No. 2, 1983

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Orthogonal polynomials associated with the Rogers-Ramanujan continued fraction

Waleed A. Al-Salam and Mourad Ismail

Vol. 104 (1983), No. 2, 269–283
Abstract

We characterize the symmetric orthogonal polynomials {Pn(x)} such that {Pn(qnx)} is also orthogonal. This leads to orthogonal polynomials related to the denominator polynomials of the continued fractions of Rogers, Ramanujan, and Carlitz. We establish the orthogonality relation for these polynomials and show that the function Σ0qn2 zn(q;q)n that appear in the aforementioned continued fractions have only real and simple zeros.

Mathematical Subject Classification
Primary: 33A65, 33A65
Milestones
Received: 21 April 1981
Published: 1 February 1983
Authors
Waleed A. Al-Salam
Mourad Ismail