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1988•Canadian Journal of MathematicsOpen access

On the Askey-Wilson and Rogers Polynomials

Mourad E. H. Ismail, Dennis Stanton

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Abstract

The q-shifted factorial (a)n or (a; q)n is and an empty product is interpreted as 1. Recently, Askey and Wilson [6] introduced the polynomials 1.1 where 1.2 and 1.3 We shall refer to these polynomials as the Askey-Wilson polynomials or the orthogonal 4ϕ3 polynomials. They generalize the 6 — j symbols and are the most general classical orthogonal polynomials, [2].

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The q-shifted factorial (a)n or (a; q)n is and an empty product is interpreted as 1. Recently, Askey and Wilson [6] introduced the polynomials 1.1 where 1.2 and 1.3 We shall refer to these polynomials as the Askey-Wilson polynomials or the orthogonal 4ϕ3 polynomials. They generalize the 6 — j symbols and are the most general classical orthogonal polynomials, [2].

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Available abstract

The q-shifted factorial (a)n or (a; q)n is and an empty product is interpreted as 1. Recently, Askey and Wilson [6] introduced the polynomials 1.1 where 1.2 and 1.3 We shall refer to these polynomials as the Askey-Wilson polynomials or the orthogonal 4ϕ3 polynomials. They generalize the 6 — j symbols and are the most general classical orthogonal polynomials, [2].

Key concepts: Askey–Wilson polynomials, Mathematics, Orthogonal polynomials, Wilson polynomials, Discrete orthogonal polynomials, Classical orthogonal polynomials, Hahn polynomials, Macdonald polynomials

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