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We investigate the use of orthonormal polynomials over the unit disk B_2 inR^2 and the unit ball B_3 in R^3. An efficient evaluation of an orthonormalpolynomial basis is given, and it is used in evaluating general polynomialsover B_2 and B_3. The least squares approximation of a function f on the unitdisk by polynomials of a given degree is investigated, including how to write apolynomial using the orthonormal basis. Matlab codes are given.

Evaluating Polynomials Over the Unit Disk and the Unit Ball