A note on \(q\)-partial differential equations for generalized \(q\)-2D Hermite polynomials

DOI10.1007/978-3-030-60107-2_8zbMath1472.39013OpenAlexW3119966768MaRDI QIDQ2050472

Li-Ping Cai, Jian Cao, Tian Xin Cai

Publication date: 31 August 2021

Full work available at URL: https://doi.org/10.1007/978-3-030-60107-2_8

zbMATH Keywords

generating function\(q\)-partial differential equationgeneralized \(q\)-2d Hermite polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Difference equations, scaling ((q)-differences) (39A13) Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable (33D50) Partial difference equations (39A14)

Related Items (1)

Post-quantum complex Itô-Hermite polynomials

Cites Work

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• Kibble-Slepian formula and generating functions for 2D polynomials
• Homogeneous \(q\)-partial difference equations and some applications
• New proofs of generating functions for Rogers-Szegö polynomials
• The linear \(q\)-difference equation \(y(x)=ay(qx)+f(x)\)
• Twin iterative positive solutions of fractional \(q\)-difference Schrödinger equations
• Some iterated fractional \(q\)-integrals and their applications
• Lectures on the theory of functions of several complex variables. Notes by Raghavan Narasimhan. Reprint
• On a system of partial differential equations and the bivariate Hermite polynomials
• Operational formulae for the complex Hermite polynomialsH_p,q(z, z¯)
• On the $q$-partial differential equations and $q$-series
• Modular structures on trace class operators and applications to Landau levels
• Complex and real Hermite polynomials and related quantizations
• Laguerre 2D-functions and their application in quantum optics
• Transformations of Laguerre 2D polynomials with applications to quasiprobabilities
• Complex Hermite polynomials: Their combinatorics and integral operators
• The bivariate Rogers–Szegö polynomials
• On some 2𝐷 orthogonal 𝑞-polynomials
• Some Orthogonal q‐Polynomials
• Some polynomials related to theta functions

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