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Orthogonal Polynomials with Symmetry of Order Three

Published online by Cambridge University Press:  20 November 2018

Charles F. Dunkl
Charles F. Dunkl*
Affiliation:
University of Virginia, Charlottesville, Virginia
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The measure (x1x2x3)2adm(x) on the unit sphere in R3 is invariant under sign-changes and permutations of the coordinates; here dm denotes the rotation-invariant surface measure. The more general measure

corresponds to the measure

on the triangle

(where ). Appell ([1] Chap. VI) constructed a basis of polynomials of degree n in v1, v2 orthogonal to all polynomials of lower degree, and a biorthogonal set for the case γ = 0. Later Fackerell and Littler [6] found a biorthogonal set for Appell's polynomials for γ ≠ 0. Meanwhile Pronol [10] had constructed an orthogonal basis in terms of Jacobi polynomials.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 4 , 01 August 1984 , pp. 685 - 717
Copyright
Copyright © Canadian Mathematical Society 1984

References

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