Computing with differential-difference operators

DOI10.1006/jsco.1997.0341zbMath0946.65009OpenAlexW2056524274MaRDI QIDQ1971740

Charles F. Dunkl

Publication date: 10 October 2000

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.1997.0341

zbMATH Keywords

harmonic polynomialsDunkl operatorsdifferential-difference operatorspolynomial arithmeticmapleabelian reflection groups

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Computation of special functions and constants, construction of tables (65D20) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (5)

The quantum harmonic oscillator with icosahedral symmetry and some explicit wavefunctions ⋮ The \(B_2\) harmonic oscillator with reflections and superintegrability ⋮ A higher rank Racah algebra and the $\mathbb{Z}_2^n$ Laplace–Dunkl operator ⋮ The dunkel intertwining operator on spaces of functions and distributions and integral representation of its dual ⋮ Derivatives of generalized Fourier expansions on the sphere

Uses Software

• Maple

Cites Work

• Unnamed Item
• Intertwining operators and polynomials associated with the symmetric group
• Product formulas and associated hypergroups for orthogonal polynomials on the simplex and on a parabolic biangle
• Reflection groups and orthogonal polynomials on the sphere
• Exact operator solution of the Calogero-Sutherland model
• Families of Orthogonal and Biorthogonal Polynomials on theN-Sphere
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres
• Common algebraic structure for the Calogero - Sutherland models
• The Addition Formula for Jacobi Polynomials and Spherical Harmonics
• Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems

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