Abstract
In this paper, we study the homogeneous polynomials orthogonal with the weight function h(x(d))=x 2k1 ...x 2kd 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 [2], and can be regarded as an extension of [1] under the weighted case.
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Supported by the National Natural Science Foundation of China (No. 10271022, and the Natural Science Foundation of Guangdong Province, China(No. 021755).
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Renhong, W., Heng, Z. On a set ofh-harmonic homogeneous polynomials. Anal. Theory Appl. 19, 234–237 (2003). https://doi.org/10.1007/BF02835282
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DOI: https://doi.org/10.1007/BF02835282