On a set ofh-harmonic homogeneous polynomials
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In this paper, we study the homogeneous polynomials orthogonal with the weight function h(x(d))=x 1 2k ...x d 2k on Sd−1. We obtain the explicit formula on a basis of the orthogonal homogeneous polynomials of degree n. It is simpler than the formula in , and can be regarded as an extension of  under the weighted case.
Key Wordsh-harmonic homogeneous polynomials weight functions
AMS(2000) subject classification43C05 33C55
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- Dunkl, C. F. and Xu, Y., Orthogonal Polynomials of Several Variables, Cambridge Univ. Press, 2001.Google Scholar