Recurrence formulas for multivariate orthogonal polynomials

Xu, Yuan

doi:10.1090/S0025-5718-1994-1212269-X

Recurrence formulas for multivariate orthogonal polynomials
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Math. Comp. 62 (1994), 687-702 Request permission

Abstract:

In this paper, necessary and sufficient conditions are given so that multivariate orthogonal polynomials can be generated by a recurrence formula. As a consequence, orthogonal polynomials of total degree n in d variables that have $\dim \Pi _n^d$ common zeros can now be constructed recursively. The result is important to the construction of Gaussian cubature formulas.

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