Bivariate version of the Hahn-Sonine theorem
نویسندگان
چکیده
منابع مشابه
Bivariate Version of the Hahn-sonine Theorem
We consider orthogonal polynomials in two variables whose derivatives with respect to x are orthogonal. We show that they satisfy a system of partial differential equations of the form α(x, y)∂ x −→ Un + β(x, y)∂x −→ Un = Λn −→ Un, where degα ≤ 2, deg β ≤ 1, −→U n = (Un0, Un−1,1, · · · , U0n) is a vector of polynomials in x and y for n ≥ 0, and Λn is an eigenvalue matrix of order (n+ 1)× (n+ 1)...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05648-3