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Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical multivariate orthogonal polynomials on the ball with our family of orthogonal polynomials. Then, using the representation of these polynomials in terms of spherical harmonics, algebraic and differential properties will be deduced.
Keywords: multivariate orthogonal polynomials; unit ball; partial differential equations. 
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Clotilde Martínez; Miguel A. Piñar. Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a19/

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