Computing with Differential-difference Operators
Copyright policy )Computing with Differential-difference Operators
The paper shows how Maple can be used to prove identities in the algebra generated be differential-difference operators (Dunkl operators), multiplication by coordinate functions and group translation, essentially in polynomial arithmetic. The proposed technique allows a conceptual proof of a complete orthogonal decomposition of the harmonic polynomials associated with a special case (the abelian reflection groups).
- Department of mathematics University of Virginia United States
- University of Virginia United States
Dunkl operators, Algebra and Number Theory, abelian reflection groups, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Connections of hypergeometric functions with groups and algebras, and related topics, Symbolic computation and algebraic computation, polynomial arithmetic, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Computational Mathematics, Computation of special functions and constants, construction of tables, maple, differential-difference operators, harmonic polynomials
Dunkl operators, Algebra and Number Theory, abelian reflection groups, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Connections of hypergeometric functions with groups and algebras, and related topics, Symbolic computation and algebraic computation, polynomial arithmetic, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Computational Mathematics, Computation of special functions and constants, construction of tables, maple, differential-difference operators, harmonic polynomials
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