Dual addition formulas: the case of continuous \(q\)-ultraspherical and \(q\)-Hermite polynomials

DOI10.1007/s11139-021-00426-7zbMath1530.33021arXiv1803.09636OpenAlexW3165859250WikidataQ113900575 ScholiaQ113900575MaRDI QIDQ6098222

Koornwinder, Tom H.

Publication date: 13 June 2023

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.09636

zbMATH Keywords

\(q\)-Racah polynomialscontinuous \(q\)-ultraspherical polynomialscontinuous \(q\)-Hermite polynomialsdual addition formulas

Mathematics Subject Classification ID

Iteration theory, iterative and composite equations (39B12) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Cites Work

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• Matrix-valued orthogonal polynomials related to \((\mathrm{SU}(2) \times \mathrm{SU}(2), \mathrm{diag})\). II
• Explicit matrix inverses for lower triangular matrices with entries involving continuous \(q\)-ultraspherical polynomials
• Some inverse relations
• Generalized Burchnall-type identities for orthogonal polynomials and expansions
• Matrix-valued orthogonal polynomials related to the quantum analogue of \((\mathrm{SU}(2) \times \mathrm{SU}(2), \text{diag})\)
• Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
• The product of two ultraspherical polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Product and Addition Formulas for the Continuous q-Ultraspherical Polynomials
• A new matrix inverse
• Dual Addition Formulas Associated with Dual Product Formulas
• Some polynomials related to theta functions
• Some polynomials related to theta functions

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