小q雅可比多项式

小q-雅可比多项式(Little q-Jacobi polynomials)是一个以基本超几何函数定义的正交多项式，定义如下.

$p_n(x;a,b;q)={}_2{\varphi }_1(q^{-n},ab{q}^{n+1};aq;q,xq)$

例子

k=3,

$p=1+q\ast x/((1-a\ast q)\ast (1-q))-q^2\ast x\ast a\ast b\ast q^n/((1-a\ast q)\ast (1-q))-q\ast x/((1-a\ast q)\ast (1-q)\ast q^n)+q^2\ast x\ast a\ast b/((1-a\ast q)\ast (1-q))$ $(1-q^{(}-n))\ast (1-q^{(}-n)\ast q)\ast (1-a\ast b\ast q^{(}n+1))\ast (1-a\ast b\ast q^{(}n+1)\ast q)\ast q^2\ast x^2/((1-a\ast q)\ast (1-a\ast q^2)\ast (1-q)\ast (1-q^2))$ $+(1-q^{(}-n))\ast (1-q^{(}-n)\ast q)\ast (1-q^{(}-n)\ast q^2)\ast (1-a\ast b\ast q^{(}n+1))\ast (1-a\ast b\ast q^{(}n+1)\ast q)\ast (1-a\ast b\ast q^{(}n+1)\ast q^2)\ast q^3\ast x^3/((1-a\ast q)\ast (1-a\ast q^2)\ast (1-a\ast q^3)\ast (1-q)\ast (1-q^2)\ast (1-q^3))$

图集

LITTLE Q-JACOBI POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT

LITTLE Q-JACOBI POLYNOMIALS IM COMPLEX 3D MAPLE PLOT

LITTLE Q-JACOBI POLYNOMIALS RE COMPLEX 3D MAPLE PLOT

LITTLE Q-JACOBI POLYNOMIALS ABS DENSITY MAPLE PLOT

LITTLE Q-JACOBI POLYNOMIALS IM DENSITY MAPLE PLOT

LITTLE Q-JACOBI POLYNOMIALS RE DENSITY MAPLE PLOT