Dual addition formulas: the case of continuous q-ultraspherical and q-Hermite polynomials
Copyright policy )Dual addition formulas: the case of continuous q-ultraspherical and q-Hermite polynomials
AbstractWe settle the dual addition formula for continuous q-ultraspherical polynomials as an expansion in terms of special q-Racah polynomials for which the constant term is given by the linearization formula for the continuous q-ultraspherical polynomials. In a second proof we derive the dual addition formula from the Rahman–Verma addition formula for these polynomials by using the self-duality of the polynomials. We also consider the limit case of continuous q-Hermite polynomials.
- University of Amsterdam Netherlands
- UNIVERSITEIT VAN AMSTERDAM Netherlands
\(q\)-Racah polynomials, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), 33.D45, dual addition formulas, continuous \(q\)-Hermite polynomials, 510, 004, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Iteration theory, iterative and composite equations, continuous \(q\)-ultraspherical polynomials
\(q\)-Racah polynomials, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), 33.D45, dual addition formulas, continuous \(q\)-Hermite polynomials, 510, 004, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Iteration theory, iterative and composite equations, continuous \(q\)-ultraspherical polynomials
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