Roelof Koekoek, Peter A.Lesky,ReneF.Swarttouw,Hypergeometric Orthogonal Polynomials ad Their q=Aalogues, Springer,2008.
十月 23, 2023
哈恩多项式, hahn, polynomials, 是一个以德国数学家wolfgang, hahn命名的正交多项式, 由下列广义超几何函数定义, displaystyle, alpha, beta, alpha, beta, alpha, 前几个为, 2970, 1980, displaystyle, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alp. 哈恩多项式 Hahn polynomials 是一个以德国数学家Wolfgang Hahn命名的正交多项式 由下列广义超几何函数定义 1 哈恩多项式 Q n x a b N 3 F 2 n x n a b 1 a 1 N 1 1 displaystyle Q n x alpha beta N 3 F 2 n x n alpha beta 1 alpha 1 N 1 1 前几个哈恩多项式为 h 5 1 27 x 4 a 4 3 x a 4 a 4 270 x 2 4 a 4 3 a 6 57 x 2 a 4 a 4 3 a 6 270 x 4 a 4 3 a 6 57 x a 4 a 4 3 a 6 3 x 2 a 2 4 a 4 3 a 6 3 x a 2 4 a 4 3 a 6 990 x 3 4 a 4 3 a 6 2 a 6 299 x 3 a 4 a 4 3 a 6 2 a 6 2970 x 2 4 a 4 3 a 6 2 a 6 897 x 2 a 4 a 4 3 a 6 2 a 6 30 x 3 a 2 4 a 4 3 a 6 2 a 6 90 x 2 a 2 4 a 4 3 a 6 2 a 6 1980 x 4 a 4 3 a 6 2 a 6 598 x a 4 a 4 3 a 6 2 a 6 60 x a 2 4 a 4 3 a 6 2 a 6 x 3 a 3 4 a 4 3 a 6 2 a 6 3 x 2 a 3 4 a 4 3 a 6 2 a 6 2 x a 3 4 a 4 3 a 6 2 a 6 displaystyle h 5 1 27 x 4 alpha 4 3 x alpha 4 alpha 4 270 x 2 4 alpha 4 3 alpha 6 57 x 2 alpha 4 alpha 4 3 alpha 6 270 x 4 alpha 4 3 alpha 6 57 x alpha 4 alpha 4 3 alpha 6 3 x 2 alpha 2 4 alpha 4 3 alpha 6 3 x alpha 2 4 alpha 4 3 alpha 6 990 x 3 4 alpha 4 3 alpha 6 2 alpha 6 299 x 3 alpha 4 alpha 4 3 alpha 6 2 alpha 6 2970 x 2 4 alpha 4 3 alpha 6 2 alpha 6 897 x 2 alpha 4 alpha 4 3 alpha 6 2 alpha 6 30 x 3 alpha 2 4 alpha 4 3 alpha 6 2 alpha 6 90 x 2 alpha 2 4 alpha 4 3 alpha 6 2 alpha 6 1980 x 4 alpha 4 3 alpha 6 2 alpha 6 598 x alpha 4 alpha 4 3 alpha 6 2 alpha 6 60 x alpha 2 4 alpha 4 3 alpha 6 2 alpha 6 x 3 alpha 3 4 alpha 4 3 alpha 6 2 alpha 6 3 x 2 alpha 3 4 alpha 4 3 alpha 6 2 alpha 6 2 x alpha 3 4 alpha 4 3 alpha 6 2 alpha 6 h 6 1 27 x 5 a 5 3 x a 5 a 5 270 x 2 5 a 5 4 a 8 57 x 2 a 5 a 5 4 a 8 270 x 5 a 5 4 a 8 57 x a 5 a 5 4 a 8 3 x 2 a 2 5 a 5 4 a 8 3 x a 2 5 a 5 4 a 8 990 x 3 5 a 5 4 a 8 3 a 9 299 x 3 a 5 a 5 4 a 8 3 a 9 2970 x 2 5 a 5 4 a 8 3 a 9 897 x 2 a 5 a 5 4 a 8 3 a 9 30 x 3 a 2 5 a 5 4 a 8 3 a 9 90 x 2 a 2 5 a 5 4 a 8 3 a 9 1980 x 5 a 5 4 a 8 3 a 9 598 x a 5 a 5 4 a 8 3 a 9 60 x a 2 5 a 5 4 a 8 3 a 9 x 3 a 3 5 a 5 4 a 8 3 a 9 3 x 2 a 3 5 a 5 4 a 8 3 a 9 2 x a 3 5 a 5 4 a 8 3 a 9 displaystyle h 6 1 27 x 5 alpha 5 3 x alpha 5 alpha 5 270 x 2 5 alpha 5 4 alpha 8 57 x 2 alpha 5 alpha 5 4 alpha 8 270 x 5 alpha 5 4 alpha 8 57 x alpha 5 alpha 5 4 alpha 8 3 x 2 alpha 2 5 alpha 5 4 alpha 8 3 x alpha 2 5 alpha 5 4 alpha 8 990 x 3 5 alpha 5 4 alpha 8 3 alpha 9 299 x 3 alpha 5 alpha 5 4 alpha 8 3 alpha 9 2970 x 2 5 alpha 5 4 alpha 8 3 alpha 9 897 x 2 alpha 5 alpha 5 4 alpha 8 3 alpha 9 30 x 3 alpha 2 5 alpha 5 4 alpha 8 3 alpha 9 90 x 2 alpha 2 5 alpha 5 4 alpha 8 3 alpha 9 1980 x 5 alpha 5 4 alpha 8 3 alpha 9 598 x alpha 5 alpha 5 4 alpha 8 3 alpha 9 60 x alpha 2 5 alpha 5 4 alpha 8 3 alpha 9 x 3 alpha 3 5 alpha 5 4 alpha 8 3 alpha 9 3 x 2 alpha 3 5 alpha 5 4 alpha 8 3 alpha 9 2 x alpha 3 5 alpha 5 4 alpha 8 3 alpha 9 目录 1 正交性 2 归递关系 3 极限关系 4 参考文献正交性 编辑对于a displaystyle alpha nbsp gt 1 和 b displaystyle beta nbsp gt 1 以及 a displaystyle alpha nbsp lt N b displaystyle beta nbsp lt N 下列正交关系成立 2 x 0 N a x x displaystyle sum x 0 N alpha x choose x nbsp b N x N x Q m x a b N Q n x a b N 1 n n a b 1 N 1 b 1 n n 2 n a b 1 a 1 n N n N d m n displaystyle beta N x choose N x Q m x alpha beta N Q n x alpha beta N frac 1 n n alpha beta 1 N 1 beta 1 n n 2n alpha beta 1 alpha 1 n N n N delta mn nbsp 归递关系 编辑哈恩多项式满足下列归递关系 3 x Q n x displaystyle x Q n x nbsp A n Q n 1 x displaystyle A n Q n 1 x nbsp A n C n Q n x displaystyle A n C n Q n x nbsp C n Q n 1 x displaystyle C n Q n 1 x nbsp 其中Q n x Q n x a b N displaystyle Q n x Q n x alpha beta N nbsp 极限关系 编辑拉卡多项式 哈恩多项式 4 lim d R n l x a b N 1 d Q n x a b N displaystyle lim delta to infty R n lambda x alpha beta N 1 delta Q n x alpha beta N nbsp 哈恩多项式 雅可比多项式lim N Q n N x a b N P n a b 1 2 x P n a b 1 displaystyle lim N to infty Q n Nx alpha beta N frac P n alpha beta 1 2x P n alpha beta 1 nbsp 参考文献 编辑 Roelof Koekoek Peter A Lesky and Rene F Swarttouw 2010 14 Roelof Koekoek p204 Roelof KoeKoek p204 Roelof p206 207Roelof Koekoek Peter A Lesky ReneF Swarttouw Hypergeometric Orthogonal Polynomials ad Their q Aalogues Springer 2008 取自 https zh wikipedia org w index php title 哈恩多项式 amp oldid 77723291, 维基百科，wiki，书籍，书籍，图书馆，
