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大q雅可比多项式

大q-雅可比多项式(英語:Big q-Jacobi polynomials)是一个以基本超几何函数定义的正交多项式[1]

BIG Q JACOBI 2D Maple PLOT

正交性 编辑

大q-雅可比多项式满足下列正交关系

 

极限关系 编辑

大q雅可比多项式→大q拉盖尔多项式

令大q雅可比多项式中的 ,即得大q拉盖尔多项式

 

图集 编辑

 
BIG Q JACOBI ABS COMPLEX3D Maple PLOT2
 
BIG Q JACOBI IM COMPLEX3D Maple PLOT
 
BIG Q JACOBI RE COMPLEX3D Maple PLOT
 
BIG Q JACOBI ABS COMPLEX DENSITY Maple PLOT
 
BIG Q JACOBI IM COMPLEX DENSITY Maple PLOT
 
BIG Q JACOBI RE COMPLEX DENSITY Maple PLOT

参考文献 编辑

  • Andrews, George E.; Askey, Richard, Classical orthogonal polynomials, Brezinski, C.; Draux, A.; Magnus, Alphonse P.; Maroni, Pascal; Ronveaux, A. (编), Polynômes orthogonaux et applications. Proceedings of the Laguerre symposium held at Bar-le-Duc, October 15–18, 1984., Lecture Notes in Math. 1171, Berlin, New York: Springer-Verlag: 36–62, 1985, ISBN 978-3-540-16059-5, MR 0838970, doi:10.1007/BFb0076530 
  • 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, René 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, René 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 
  1. ^ Roelof p438

大q雅可比多项式, 大q, 雅可比多项式, 英語, jacobi, polynomials, 是一个以基本超几何函数定义的正交多项式, jacobi, maple, plotp, displaystyle, displaystyle, 目录, 正交性, 极限关系, 图集, 参考文献正交性, 编辑大q, 雅可比多项式满足下列正交关系, displaystyle, delta, nbsp, 极限关系, 编辑, 大q拉盖尔多项式令中的b, displaystyle, nbsp, 即得大q拉盖尔多项式p, displays. 大q 雅可比多项式 英語 Big q Jacobi polynomials 是一个以基本超几何函数定义的正交多项式 1 BIG Q JACOBI 2D Maple PLOTP n x a b c q 3 ϕ 2 q n a b q n 1 x a q c q q q displaystyle displaystyle P n x a b c q 3 phi 2 q n abq n 1 x aq cq q q 目录 1 正交性 2 极限关系 3 图集 4 参考文献正交性 编辑大q 雅可比多项式满足下列正交关系 x p n x p m x x v x h n d m n displaystyle sum x p n x p m x x v x h n delta m n nbsp 极限关系 编辑大q雅可比多项式 大q拉盖尔多项式令大q雅可比多项式中的b 0 displaystyle b 0 nbsp 即得大q拉盖尔多项式P n x a 0 c q P n x a c q displaystyle P n x a 0 c q P n x a c q nbsp 图集 编辑 nbsp BIG Q JACOBI ABS COMPLEX3D Maple PLOT2 nbsp BIG Q JACOBI IM COMPLEX3D Maple PLOT nbsp BIG Q JACOBI RE COMPLEX3D Maple PLOT nbsp BIG Q JACOBI ABS COMPLEX DENSITY Maple PLOT nbsp BIG Q JACOBI IM COMPLEX DENSITY Maple PLOT nbsp BIG Q JACOBI RE COMPLEX DENSITY Maple PLOT参考文献 编辑Andrews George E Askey Richard Classical orthogonal polynomials Brezinski C Draux A Magnus Alphonse P Maroni Pascal Ronveaux A 编 Polynomes orthogonaux et applications Proceedings of the Laguerre symposium held at Bar le Duc October 15 18 1984 Lecture Notes in Math 1171 Berlin New York Springer Verlag 36 62 1985 ISBN 978 3 540 16059 5 MR 0838970 doi 10 1007 BFb0076530 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 Roelof p438 取自 https zh wikipedia org w index php title 大q雅可比多项式 amp oldid 79102475, 维基百科,wiki,书籍,书籍,图书馆,

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