Homogeneous \(q\)-partial difference equations and some applications

DOI10.1016/j.aam.2016.11.001zbMath1392.11014OpenAlexW2555076617MaRDI QIDQ730311

Jian Cao

Publication date: 27 December 2016

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2016.11.001

zbMATH Keywords

generating functionAndrews-Askey integral\(q\)-hypergeometric polynomialAskey-Roy integralhomogeneous \(q\)-partial difference equationmoment integralRamanujan's integral

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Difference equations, scaling ((q)-differences) (39A13)

Related Items (8)

Generalized q-Laguerre type polynomials and q-partial differential equations ⋮ Multiple expansion formulas over root systems ⋮ On multiplicity of solutions to nonlinear partial difference equations with delay ⋮ \((q,c)\)-derivative operator and its applications ⋮ Nevanlinna theory for Jackson difference operators and entire solutions of \(q\)-difference equations ⋮ A note on \(q\)-partial differential equations for generalized \(q\)-2D Hermite polynomials ⋮ q-Laguerre polynomials and related q-partial differential equations ⋮ q-Difference equations for the generalized Cigler’s polynomials

Cites Work

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• Homogeneous \(q\)-difference equations and generating functions for \(q\)-hypergeometric polynomials
• Kibble-Slepian formula and generating functions for 2D polynomials
• A \(q\)-extension of a partial differential equation and the Hahn polynomials
• Poisson kernel and multilinear generating functions of some orthogonal polynomials
• Generalizations of Milne's \(\mathrm{U}(n+1)q\)-binomial theorems
• Expansion of analytic functions in \(q\)-orthogonal polynomials
• More q-beta integrals
• Balanced \(_ 3\phi_ 2\) summation theorems for \(U(n)\) basic hypergeometric series
• \(q\)-Taylor theorems, polynomial expansions, and interpolation of entire functions.
• Applications of a generalized \(q\)-difference equation
• A note on generalized \(q\)-difference equations for \(q\)-beta and Andrews-Askey integral
• Notes on Askey-Roy integral and certain generating functions for \(q\)-polynomials
• A note on moment integrals and some applications
• Generating functions for certain q-orthogonal polynomials
• Lectures on the theory of functions of several complex variables. Notes by Raghavan Narasimhan. Reprint
• A remark on Andrews-Askey integral
• The homogeneous \(q\)-difference operator
• Operational formulae for the complex Hermite polynomialsH_p,q(z, z¯)
• A Note onq-Integrals and Certain Generating Functions
• On the $q$-partial differential equations and $q$-series
• Twoq-difference equations andq-operator identities
• An extension of the non-terminating₆φ₅summation and the Askey–Wilson polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Complex and real Hermite polynomials and related quantizations
• Another q-Extension of the Beta Function
• Two Integrals of Ramanujan
• Applications of Basic Hypergeometric Functions
• Barnes and Ramanujan-Type Integrals on the q-Linear Lattice
• Two expansion formulas involving the Rogers–Szegő polynomials with applications
• Some Orthogonal q‐Polynomials
• Summations and Transformations for Basic Appell Series

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