摘要
In this paper, we study the homogeneous polynomials orthogonal with the weight function h(x (d))=x 2k 1 1…x 2k d d on S d-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.
In this paper, we study the homogeneous polynomials orthogonal with the weight function h(x (d))=x 2k 1 1…x 2k d d on S d-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.
基金
Supported by the National Natural Science Foundation of China( No. 1 0 2 71 0 2 2 ,and the NaturalScience Foundation of Guangdong Province,China( No.0 2 1 75 5 )
