More on the q-oscillator algebra and q-orthogonal polynomials
Copyright policy )More on the q-oscillator algebra and q-orthogonal polynomials
Properties of certain $q$-orthogonal polynomials are connected to the $q$-oscillator algebra. The Wall and $q$-Laguerre polynomials are shown to arise as matrix elements of $q$-exponentials of the generators in a representation of this algebra. A realization is presented where the continuous $q$-Hermite polynomials form a basis of the representation space. Various identities are interpreted within this model. In particular, the connection formula between the continuous big $q$-Hermite polynomials and the continuous $q$-Hermite polynomials is thus obtained, and two generating functions for these last polynomials are algebraically derived.
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Mathematics - Classical Analysis and ODEs, \(q\)-oscillator, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), Quantum groups (quantized enveloping algebras) and related deformations, Applications of basic hypergeometric functions, \(q\)-orthogonal polynomials, Quantum groups and related algebraic methods applied to problems in quantum theory
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Mathematics - Classical Analysis and ODEs, \(q\)-oscillator, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), Quantum groups (quantized enveloping algebras) and related deformations, Applications of basic hypergeometric functions, \(q\)-orthogonal polynomials, Quantum groups and related algebraic methods applied to problems in quantum theory
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