### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 020, 11 pages      arXiv:1511.07056      https://doi.org/10.3842/SIGMA.2016.020
Contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications

### Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations

Clotilde Martínez and Miguel A. Piñar

Received November 24, 2015, in final form February 18, 2016; Published online February 23, 2016

Abstract
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.

Key words: multivariate orthogonal polynomials; unit ball; partial differential equations.

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