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

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