QMEIXNER-POLLACZEK 2D PLOT
Q梅西纳-帕拉泽克多项式定义如下:[1]
![{\displaystyle P_{n}(x;a|q)=a^{-n}e^{in\phi }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c7ea2d6436c468a6644497c36a35926151f4838b)
![{\displaystyle {\frac {a^{2};q_{n}}{(q;q)_{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c6f383cef38db1a5a2c90308331a2a0ae7e2680c)
极限关系[编辑]
连续q哈恩多项式→Q梅西纳-帕拉泽克多项式
Q梅西纳-帕拉泽克多项式→连续q超球面多项式
Q梅西纳-帕拉泽克多项式→连续q拉盖尔多项式
![{\displaystyle P_{n}(cos(\theta +\phi );q^{\alpha /2+1/2}|q)=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ecfa4317c12c97fba64a6caaf75ebc21994b4234)
QMEIXNER-POLLACZEK ABS COMPLEX 3D MAPLE PLOT
|
QMEIXNER-POLLACZEK IM COMPLEX 3D MAPLE PLOT
|
QMEIXNER-POLLACZEK RE COMPLEX 3D MAPLE PLOT
|
QMEIXNER-POLLACZEK ABS DENSITY MAPLE PLOT
|
QMEIXNER-POLLACZEK IM DENSITY MAPLE PLOT
|
QMEIXNER-POLLACZEK 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, 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, 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, Hypergeometric Orthogonal Polynomials and its q-Analoques, p460,Springer