Gasper, George; Rahman, Mizan, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications 96 2nd, Cambridge University Press, 2004, ISBN 978-0-521-83357-8, MR 2128719, doi:10.2277/0521833574
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二月 16, 2024
q拉盖尔多项式, q拉盖尔多项式是一个以基本超几何函数和q阶乘幂定义的正交多项式, laguerre, polynomialsl, displaystyle, displaystyle, alpha, frac, alpha, alpha, alpha, 目录, 正交性, 极限关系, 图集, 参考文献正交性, 编辑q, 拉盖尔多项式满足下列正交关系, displaystyle, alpha, alpha, alpha, infty, frac, alpha, nbsp, 极限关系, 编辑小q雅可比多项式, 在校q雅. q拉盖尔多项式是一个以基本超几何函数和Q阶乘幂定义的正交多项式 q Laguerre PolynomialsL n a x q q a 1 q n q q n 1 ϕ 1 q n q a 1 q q n a 1 x displaystyle displaystyle L n alpha x q frac q alpha 1 q n q q n 1 phi 1 q n q alpha 1 q q n alpha 1 x 目录 1 正交性 2 极限关系 3 图集 4 参考文献正交性 编辑Q 拉盖尔多项式满足下列正交关系 a b L n a x q L m a x q x a x q d x q a 1 q n q q n q n displaystyle int a b L n alpha x q L m alpha x q x alpha x q infty dx frac q alpha 1 q n q q n q n nbsp 极限关系 编辑小q雅可比多项式 Q拉盖尔多项式 在校q雅可比多项式的定义中 令a q a displaystyle a q alpha nbsp 以及x b 1 q 1 displaystyle x to b 1 q 1 nbsp 并令b displaystyle b to infty nbsp 即得q拉盖尔多项式 Q梅西纳多项式 Q拉盖尔多项式 令Q梅西纳多项式中b q a displaystyle b q alpha nbsp 以及q x c q a x displaystyle q x cq alpha x nbsp 然后取c displaystyle c to infty nbsp 即得Q拉盖尔多项式 lim c M n c q a x q a c q q q n q a 1 q n displaystyle lim c to infty M n cq alpha x q alpha c q frac q q n q alpha 1 q n nbsp 图集 编辑下列 L 5 3 7 x i y q displaystyle displaystyle L 5 3 7 x iy q nbsp 图 以q 为可变参数 nbsp Q LAGUERRE POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT nbsp Q LAGUERRE POLYNOMIALS IM COMPLEX 3D MAPLE PLOT nbsp Q LAGUERRE POLYNOMIALS RE COMPLEX 3D MAPLE PLOT nbsp Q LAGUERRE POLYNOMIALS ABS DENSITY MAPLE PLOT nbsp Q LAGUERRE POLYNOMIALS RE DENSITY MAPLE PLOT nbsp Q LAGUERRE POLYNOMIALS IM DENSITY MAPLE PLOT参考文献 编辑Gasper George Rahman Mizan Basic hypergeometric series Encyclopedia of Mathematics and its Applications 96 2nd Cambridge University Press 2004 ISBN 978 0 521 83357 8 MR 2128719 doi 10 2277 0521833574 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 http dlmf nist gov 18 contribution url 缺少标题 帮助 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 Moak Daniel S The q analogue of the Laguerre polynomials J Math Anal Appl 1981 81 1 20 47 MR 0618759 doi 10 1016 0022 247X 81 90048 2 取自 https zh wikipedia org w index php title Q拉盖尔多项式 amp oldid 40771755, 维基百科,wiki,书籍,书籍,图书馆,