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Q阶乘幂定义的正交多项式

q-Laguerre Polynomials

正交性

Q-拉盖尔多项式满足下列正交关系

 

极限关系

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。

 

图集

下列 : 图,以q 为可变参数。

 
Q-LAGUERRE POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT
 
Q-LAGUERRE POLYNOMIALS IM COMPLEX 3D MAPLE PLOT
 
Q-LAGUERRE POLYNOMIALS RE COMPLEX 3D MAPLE PLOT
 
Q-LAGUERRE POLYNOMIALS ABS DENSITY MAPLE PLOT
 
Q-LAGUERRE POLYNOMIALS RE DENSITY MAPLE PLOT
 
Q-LAGUERRE POLYNOMIALS IM DENSITY MAPLE PLOT

参考文献

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  • 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 
  • 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