A Taylor expansion theorem for an elliptic extension of the Askey-Wilson operator

zbMath1185.33021arXiv0803.2329MaRDI QIDQ3407975

Michael J. Schlosser

Publication date: 24 February 2010

Full work available at URL: https://arxiv.org/abs/0803.2329

zbMATH Keywords

Taylor expansionsAskey-Wilson operatorelliptic hypergeometric serieselliptic biorthogonal funcitonsFrenkel and Turaev's \(_{1-}V_9\) summationFrenkel and Turaev's \(_{12}V_{11}\) transformationnontermination \(_8\varphi_7\) summation

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Other functions defined by series and integrals (33E20) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Approximation by other special function classes (41A30) Elliptic functions and integrals (33E05)

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