\(q\)-Taylor theorems, polynomial expansions, and interpolation of entire functions.
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Publication:1399540
DOI10.1016/S0021-9045(03)00076-5zbMath1035.30025MaRDI QIDQ1399540
Mourad E. H. Ismail, Dennis W. Stanton
Publication date: 30 July 2003
Published in: Journal of Approximation Theory (Search for Journal in Brave)
integral representations\(q\)-Taylor series\(q\)-exponential functionpolynomial basesCarlson's theoremAskey-Wilson operators
Approximation in the complex plane (30E10) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Interpolation in approximation theory (41A05)
Related Items
Applications of \(q\)-Taylor theorems ⋮ Formulas and identities involving the Askey-Wilson operator ⋮ Taylor series for the Askey-Wilson operator and classical summation formulas ⋮ Semiclassical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromy ⋮ Interpolation of entire functions on regular sparse sets and \(q\)-Taylor series ⋮ Some combinatorial and analytical identities ⋮ A sampling theorem related to the Wilson transform ⋮ Bootstrapping and Askey-Wilson polynomials ⋮ On exponential and trigonometric functions on nonuniform lattices ⋮ Introduction of the numerical methods in quantum calculus with uncertainty ⋮ Basic Fourier transform on the space of entire functions of logarithm order 2 ⋮ \(q\)-fractional integral operators with two parameters ⋮ Diophantine properties of orthogonal polynomials and rational functions ⋮ \(q\)-Taylor and interpolation series for Jackson \(q\)-difference operators ⋮ On \(q\)-extension of Laurent expansion with applications ⋮ Moments of Askey-Wilson polynomials ⋮ On moments of classical orthogonal polynomials ⋮ Expansions in the Askey-Wilson polynomials ⋮ Hypergeometric origins of Diophantine properties associated with the Askey scheme ⋮ Nevanlinna theory of the Askey-Wilson divided difference operator ⋮ Wiman-Valiron theory for a polynomial series based on the Askey-Wilson operator ⋮ A Paley-Wiener theorem for the Askey-Wilson function transform ⋮ Regulary lacunary sets and entire arithmetic functions ⋮ On some \(q\)-versions of the Ramanujan master theorem ⋮ A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials ⋮ PROBABILISTIC IMPLICATIONS OF SYMMETRIES OF q-HERMITE AND AL-SALAM–CHIHARA POLYNOMIALS ⋮ A Whittaker-Shannon-Kotelnikov sampling theorem related to the Askey-Wilson functions ⋮ Homogeneous \(q\)-partial difference equations and some applications ⋮ Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths ⋮ On a family of integrals that extend the Askey-Wilson integral ⋮ A \(q\)-translation approach to Liu's calculus ⋮ q-Analogs of Lidstone expansion theorem, two-point Taylor expansion theorem, and Bernoulli polynomials ⋮ Formulae for Askey-Wilson moments and enumeration of staircase tableaux ⋮ \(q\)-type Lidstone expansions and an interpolation problem for entire functions ⋮ A 𝑞-sampling theorem and product formula for continuous 𝑞-Jacobi functions ⋮ Interpolation of entire functions, product formula for basic sine function ⋮ \(q\)-fractional Askey-Wilson integrals and related semigroups of operators
Cites Work
- Asymptotic and generating relations for the q-Jacobi and //\(4Phi_ 3\) polynomials
- About the growth of entire functions solutions of linear algebraic \(q\)- difference equations
- Diagonalization of certain integral operators
- Applications of \(q\)-Taylor theorems
- New Proofs of Some q-Series Results
- Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
- Difference Equations: Disconjugacy, Principal Solutions, Green's Functions, Complete Monotonicity
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