双Q克拉夫楚克多项式

二月 07, 2023

双Q克拉夫楚克多项式是一个以基本超几何函数定义的正交多项式^[1]

$K_{n}(\lambda (x);c,N|q)=_{3}\Phi _{2}(q^{-n},q^{-x},cq^{x-N};q^{-N},0|q;q)$

关系式

令Q拉卡多项式中 $a=b$ , $cq=q^{-N}$ 即得双Q克拉夫楚克多项式
令双q哈恩多项式中 $d=c\gamma ^{-1}q^{-N-1}$ ,且 $\gamma$ →0,即得双Q克拉夫楚克多项式
令双Q克拉夫楚克多项式 $c=1=p^{-1}$ ,并令q→1,即得克拉夫楚克多项式

图集

DUAL Q-KRAWTCHOUK POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT

DUAL Q-KRAWTCHOUK POLYNOMIALS IM COMPLEX 3D MAPLE PLOT

DUAL Q-KRAWTCHOUK POLYNOMIALS RE COMPLEX 3D MAPLE PLOT

DUAL Q-KRAWTCHOUK POLYNOMIALS ABS DENSITY MAPLE PLOT

DUAL Q-KRAWTCHOUK POLYNOMIALS IM DENSITY MAPLE PLOT

DUAL Q-KRAWTCHOUK POLYNOMIALS RE DENSITY MAPLE PLOT

参考文献

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

^ Roelof Koekoek, p505

二月 07, 2023

双q克拉夫楚克多项式, 是一个以基本超几何函数定义的正交多项式, displaystyle, lambda, 关系式, 编辑令q拉卡多项式中a, displaystyle, displaystyle, 即得, 令双q哈恩多项式中d, displaystyle, gamma, 且γ, displaystyle, gamma, 即得, 令c, displaystyle, 并令q, 即得克拉夫楚克多项式图集, 编辑, dual, krawtchouk, polynomials, complex, maple, plot,. 双Q克拉夫楚克多项式是一个以基本超几何函数定义的正交多项式 1 K n l x c N q 3 F 2 q n q x c q x N q N 0 q q displaystyle K n lambda x c N q 3 Phi 2 q n q x cq x N q N 0 q q 关系式编辑令Q拉卡多项式中a b displaystyle a b c q q N displaystyle cq q N 即得双Q克拉夫楚克多项式令双q哈恩多项式中d c g 1 q N 1 displaystyle d c gamma 1 q N 1 且g displaystyle gamma 0 即得双Q克拉夫楚克多项式令双Q克拉夫楚克多项式c 1 p 1 displaystyle c 1 p 1 并令q 1 即得克拉夫楚克多项式图集编辑 DUAL Q KRAWTCHOUK POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT DUAL Q KRAWTCHOUK POLYNOMIALS IM COMPLEX 3D MAPLE PLOT DUAL Q KRAWTCHOUK POLYNOMIALS RE COMPLEX 3D MAPLE PLOT DUAL Q KRAWTCHOUK POLYNOMIALS ABS DENSITY MAPLE PLOT DUAL Q KRAWTCHOUK POLYNOMIALS IM DENSITY MAPLE PLOT DUAL Q KRAWTCHOUK POLYNOMIALS RE 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 Roelof Koekoek p505 取自 https zh wikipedia org w index php title 双Q克拉夫楚克多项式 amp oldid 44464379, 维基百科，wiki，书籍，书籍，图书馆，

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