Multivariable Big and Little q-Jacobi Polynomials

A four-parameter family of multivariable big q-Jacobi polynomials and a three-parameter family of multivariable little q-Jacobi polynomials are introduced. For both families, full orthogonality is proved with the help of a second-order q-difference operator which is diagonalized by the multivariable...

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Veröffentlicht in:SIAM journal on mathematical analysis 1997-03, Vol.28 (2), p.452-480
1. Verfasser: Stokman, Jasper V.
Format: Artikel
Sprache:eng
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Zusammenfassung:A four-parameter family of multivariable big q-Jacobi polynomials and a three-parameter family of multivariable little q-Jacobi polynomials are introduced. For both families, full orthogonality is proved with the help of a second-order q-difference operator which is diagonalized by the multivariable polynomials. A link is made between the orthogonality measures and R. Askey's q-extensions of Selberg's multidimensional beta-integrals.
ISSN:0036-1410
1095-7154
DOI:10.1137/S0036141095287192