正交多项式的积化和差公式

Reducing a Product Term to Summation for Orthogonal Polynomials

设Π_n为n次多项式的集合,{P_n(x)}(n=0,1,…)为区间I上的正交多项式:且满足 其中w(x)为权函数,为书写简单,以下将a_(nn)记为c_n。 1.

A recurrent relation to reduce a product term to summation for general algebraic orthogonal polynomials is given. Some direct formulas for specific orthogoual polynomial, Such as Hcrmite's and Chcbyshcv's, arc also given.