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Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F., Pollaczek Polynomials, Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (编), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248
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十月 23, 2023
梅西纳, 珀拉泽克多项式, 是一个以超几何函数定义的正交多项式meixner, pollaczek, polynomials, animationmeixner, pollaczek, polynomials, animation, displaystyle, lambda, frac, lambda, lambda, lambda, displaystyle, lambda, frac, lambda, lambda, lambda, 正交性, 编辑, displaystyle, infty, infty, la. 梅西纳 珀拉泽克多项式是一个以超几何函数定义的正交多项式Meixner Pollaczek Polynomials animationMeixner Pollaczek Polynomials animation P n l x ϕ 2 l n n e i n ϕ 2 F 1 n l i x 2 l 1 e 2 i ϕ displaystyle P n lambda x phi frac 2 lambda n n e in phi 2 F 1 n lambda ix 2 lambda 1 e 2i phi P n l cos ϕ a b 2 l n n e i n ϕ 2 F 1 n l i a cos ϕ b sin ϕ 2 l 1 e 2 i ϕ displaystyle P n lambda cos phi a b frac 2 lambda n n e in phi 2 F 1 n lambda i a cos phi b sin phi 2 lambda 1 e 2i phi 正交性 编辑 P n l x ϕ P m l x ϕ w x l ϕ d x 2 p G n 2 l 2 sin ϕ 2 l n d m n displaystyle int infty infty P n lambda x phi P m lambda x phi w x lambda phi dx frac 2 pi Gamma n 2 lambda 2 sin phi 2 lambda n delta mn nbsp 极限关系 编辑连续双哈恩多项式 梅西纳 珀拉泽克多项式lim t S n x t 2 l i t l i t t c o s ϕ t n N P n l x ϕ s i n ϕ n displaystyle lim t to infty frac S n x t 2 lambda it lambda it tcos phi t n N frac P n lambda x phi sin phi n nbsp 连续哈恩多项式 梅西纳 珀拉泽克多项式lim t S n x t l i t t a n ϕ l i t t t a n ϕ t n N P n l x ϕ c o s ϕ n displaystyle lim t to infty frac S n x t lambda it tan phi lambda it ttan phi t n N frac P n lambda x phi cos phi n nbsp 梅西纳 珀拉泽克多项式 拉盖尔多项式梅西纳 珀拉泽克多项式 埃尔米特多项式参考文献 编辑Koekoek Roelof Lesky Peter A Swarttouw Rene F Hypergeometric orthogonal polynomials and their q analogues Springer Monographs in Mathematics Berlin New York Springer Verlag 2010 ISBN 978 3 642 05013 8 MR 2656096 doi 10 1007 978 3 642 05014 5 Koornwinder Tom H Wong Roderick S C Koekoek Roelof Swarttouw Rene F Pollaczek Polynomials Olver Frank W J Lozier Daniel M Boisvert Ronald F Clark Charles W 编 NIST Handbook of Mathematical Functions Cambridge University Press 2010 ISBN 978 0521192255 MR2723248 Meixner J Orthogonale Polynomsysteme Mit Einer Besonderen Gestalt Der Erzeugenden Funktion J London Math Soc 1934 s1 9 6 13 doi 10 1112 jlms s1 9 1 6 Pollaczek Felix Sur une generalisation des polynomes de Legendre Les Comptes rendus de l Academie des sciences 1949 228 1363 1365 2015 01 27 MR 0030037 原始内容存档于2017 08 06 取自 https zh wikipedia org w index php title 梅西纳 珀拉泽克多项式 amp oldid 61599074, 维基百科,wiki,书籍,书籍,图书馆,