A new approach to the theory of classical hypergeometric polynomials
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Publication:5694978
DOI10.1090/S0002-9947-04-03620-7zbMath1080.33016arXivmath/0312247OpenAlexW1893631896MaRDI QIDQ5694978
José Manuel Marco, Javier Parcet
Publication date: 6 October 2005
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0312247
Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)
Related Items (8)
Elliptic hypergeometric summations by Taylor series expansion and interpolation ⋮ Taylor series for the Askey-Wilson operator and classical summation formulas ⋮ Laplacian operators and Radon transforms on Grassmann graphs ⋮ Introduction of the numerical methods in quantum calculus with uncertainty ⋮ \(q\)-Taylor and interpolation series for Jackson \(q\)-difference operators ⋮ Nevanlinna theory for Jackson difference operators and entire solutions of \(q\)-difference equations ⋮ TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS ⋮ q-Difference linear control systems
Cites Work
- The factorization method for the Askey-Wilson polynomials
- On the natural representation of \(S({\Omega})\) into \(L ^{2}(\mathcal{P}({\Omega)})\) : Discrete harmonics and Fourier transform
- Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
- Orthogonal Polynomials, Duality and Association Schemes
- The Pearson Equation and the Beta Integrals
- A Right Inverse of the Askey-Wilson Operator
- Taylor series for the Askey-Wilson operator and classical summation formulas
- Two linear transformations each tridiagonal with respect to an eigenbasis of the other
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