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-拉盖尔多项式满足下列正交关系
- 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,令以及,并令,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,以及,然后取即得Q拉盖尔多项式。
下列 :图,以q 为可变参数。
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- 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
- 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