小q勒让德多项式

小q勒让德多项式(Little q-Legender polynomials)是一个以基本超几何函数定义的正交多项式^[1]

$P_{n}(x|q)=\;_{2}\phi _{1}\left({\begin{matrix}q^{-n}&q^{n+1}\\q\end{matrix}};q,qx\right)$

极限关系

小q勒让德多项式→勒让德多项式

$\lim _{q\to 1}p_{n}(x|q)=P_{n}(1-2x)$

LITTLE Q-LEGENDRE POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT

LITTLE Q-LEGENDRE POLYNOMIALS IM COMPLEX 3D MAPLE PLOT

LITTLE Q-LEGENDRE POLYNOMIALS RE COMPLEX 3D MAPLE PLOT

LITTLE Q-LEGENDRE POLYNOMIALS ABS DENSITY MAPLE PLOT

LITTLE Q-LEGENDRE POLYNOMIALS IM DENSITY MAPLE PLOT

LITTLE Q-LEGENDRE POLYNOMIALS RE DENSITY MAPLE PLOT

^ Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p486,Springer,2010