连续q拉盖尔多项式

连续q拉盖尔多项式(Continuous q-Laguerre polynomials)是一个以基本超几何函数定义的正交多项式[1]

3rd order Continuous q Laguerre polynomials

极限关系

Q梅西纳-帕拉泽克多项式连续q拉盖尔多项式

  

阿拉-萨拉姆-迟哈剌多项式→连续q拉盖尔多项式

令连续q拉盖尔多项式中 ,q→1,即得拉盖尔多项式

验证

3阶连续q拉盖尔多项式:  

3阶广义拉盖尔多项式:

   

两者显然相等。

图集

 
CONTINUOUS Q LAGUERRE ABS COMPLEX 3D MAPLE PLOT
 
CONTINUOUS Q LAGUERRE IM COMPLEX 3D MAPLE PLOT
 
CONTINUOUS Q LAGUERRE RE COMPLEX 3D MAPLE PLOT
 
CONTINUOUS Q LAGUERRE ABS DENSITY MAPLE PLOT
 
CONTINUOUS Q LAGUERRE IM DENSITY MAPLE PLOT
 
CONTINUOUS Q LAGUERRE RE DENSITY MAPLE PLOT

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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 
  1. ^ Roelof Koekoek, Peter Lesky, Rene Swarttouw,Hypergeometric Orthogonal Polynomials and Their q-Analogues, p514, Springer