A 𝑞-sampling theorem and product formula for continuous 𝑞-Jacobi functions
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Publication:3432775
DOI10.1090/S0002-9939-07-08717-5zbMath1122.33009MaRDI QIDQ3432775
Publication date: 18 April 2007
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) (q)-gamma functions, (q)-beta functions and integrals (33D05) Applications of basic hypergeometric functions (33D90)
Related Items (4)
Basic Fourier transform on the space of entire functions of logarithm order 2 ⋮ The finite continuous nonsymmetric Jacobi transform and applications ⋮ A Paley-Wiener theorem for the Askey-Wilson function transform ⋮ A Whittaker-Shannon-Kotelnikov sampling theorem related to the Askey-Wilson functions
Cites Work
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- A product formula for the continuous q-Jacobi polynomials
- A new proof of a Paley-Wiener type theorem for the Jacobi transform
- \(q\)-Taylor theorems, polynomial expansions, and interpolation of entire functions.
- The finite continuous Jacobi transform and its inverse
- Applications of \(q\)-Taylor theorems
- Interpolation of entire functions, product formula for basic sine function
- A Whittaker-Shannon-Kotelnikov sampling theorem related to the Askey-Wilson functions
- The Continuous (α, β)-Jacobi Transform and its Inverse when α+ β+ 1 is a Positive Integer
- The Associated Askey-Wilson Polynomials
- Some orthogonal very well poised -functions
- Some Summation Theorems and Transformations for Q-Series
- A 𝑞-analogue of the Whittaker-Shannon-Kotel’nikov sampling theorem
- The Askey–Wilson polynomials and q-Sturm–Liouville problems
- Some orthogonal very-well-poised \(_8\varphi_7\)-functions that generalize Askey-Wilson polynomials
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