Geodesic
Orthogonal Polynomials with Symmetry of Order Three
Canadian journal of mathematics, Tome 36 (1984) no. 4, pp. 685-717

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Dunkl, Charles F. Orthogonal Polynomials with Symmetry of Order Three. Canadian journal of mathematics, Tome 36 (1984) no. 4, pp. 685-717. doi: 10.4153/CJM-1984-040-1
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[1] 1. Appell, P. and de Fériet, J. Kampé, Fonctions hypergéométriques et hypersphériques, polynomes d'Hermite (Gauthier-Villars, Paris, 1926). Google Scholar

[2] 2. Bailey, W., Generalized hypergeometric series (Cambridge University Press, Cambridge, 1935). Google Scholar

[3] 3. Dunkl, C., A difference equation and Halm polynomials in two variables. Pacific J. Math. 92 (1981). 57–71. Google Scholar

[4] 4. Dunkl, C., Cube group invariant spherical harmonics and Krawtchouk polynomials. Math. Z. 777 (1981), 561–577. Google Scholar

[5] 5. Dunkl, C., Orthogonal polynomials on the sphere with octahedral symmetry. Trans. Amer. Math Soc. 282 (1984), 555–575. Google Scholar

[6] 6. Faekerell, E. and Littler, R., Polynomials biorthogonal to Appell's polynomials. Bull. Austral Math. Soc. 11 (1974), 181–195. Google Scholar

[7] 7. Koornwinder, T., Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators III, IV; Indag. Math. 36 (1974), 357–381. Google Scholar

[8] 8. Koornwinder, T., Two-variable analogues of the classical orthogonal polynomials, pp. 435–495 in Theory and applications of special functions (Academic Press, New York, 1975). Google Scholar

[9] 9. Parlett, B., The symmetric eigenvalue problem (Prentice-Hall, Englewood Cliffs, 1980). Google Scholar

[10] 10. Proriol, J., Sur une famille de polynomes à deux variables orthogonaux dans un triangle, C. R. Acad. Sci. Paris 245 (1957), 2459–2461. Google Scholar

[11] 11. Segal, M., Jacobi polynomials as invariant functions on the orthogonal group. Ph. D. thesis. University of Virginia (1978). Google Scholar

[12] 12. Szegö, G., Orthogonal polynomials, A. M. S. Colloquium Publications 23 (American Mathematical Society, Providence, 1959). Google Scholar

[13] 13. Wilson, J., Hypergeometric series, recurrence relations and some new orthogonal functions. Ph. D. thesis, University of Wisconsin-Madison (1978). Google Scholar

[14] 14. Wilson, J., Some hypergeometric orthogonal polynomials, SIAM J. Math. Anal. 11 (1980), 690–701. Google Scholar

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