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[ 1] .
p
n
(
x
;
a
,
b
;
q
)
=
2
ϕ
1
(
q
−
n
,
a
b
q
n
+
1
;
a
q
;
q
,
x
q
)
{\displaystyle \displaystyle p_{n}(x;a,b;q)={}_{2}\phi _{1}(q^{-n},abq^{n+1};aq;q,xq)}
k=3,
p
=
1
+
q
∗
x
/
(
(
1
−
a
∗
q
)
∗
(
1
−
q
)
)
−
q
2
∗
x
∗
a
∗
b
∗
q
n
/
(
(
1
−
a
∗
q
)
∗
(
1
−
q
)
)
−
q
∗
x
/
(
(
1
−
a
∗
q
)
∗
(
1
−
q
)
∗
q
n
)
+
q
2
∗
x
∗
a
∗
b
/
(
(
1
−
a
∗
q
)
∗
(
1
−
q
)
)
{\displaystyle p=1+q*x/((1-a*q)*(1-q))-q^{2}*x*a*b*q^{n}/((1-a*q)*(1-q))-q*x/((1-a*q)*(1-q)*q^{n})+q^{2}*x*a*b/((1-a*q)*(1-q))}
(
1
−
q
(
−
n
)
)
∗
(
1
−
q
(
−
n
)
∗
q
)
∗
(
1
−
a
∗
b
∗
q
(
n
+
1
)
)
∗
(
1
−
a
∗
b
∗
q
(
n
+
1
)
∗
q
)
∗
q
2
∗
x
2
/
(
(
1
−
a
∗
q
)
∗
(
1
−
a
∗
q
2
)
∗
(
1
−
q
)
∗
(
1
−
q
2
)
)
{\displaystyle (1-q^{(}-n))*(1-q^{(}-n)*q)*(1-a*b*q^{(}n+1))*(1-a*b*q^{(}n+1)*q)*q^{2}*x^{2}/((1-a*q)*(1-a*q^{2})*(1-q)*(1-q^{2}))}
+
(
1
−
q
(
−
n
)
)
∗
(
1
−
q
(
−
n
)
∗
q
)
∗
(
1
−
q
(
−
n
)
∗
q
2
)
∗
(
1
−
a
∗
b
∗
q
(
n
+
1
)
)
∗
(
1
−
a
∗
b
∗
q
(
n
+
1
)
∗
q
)
∗
(
1
−
a
∗
b
∗
q
(
n
+
1
)
∗
q
2
)
∗
q
3
∗
x
3
/
(
(
1
−
a
∗
q
)
∗
(
1
−
a
∗
q
2
)
∗
(
1
−
a
∗
q
3
)
∗
(
1
−
q
)
∗
(
1
−
q
2
)
∗
(
1
−
q
3
)
)
{\displaystyle +(1-q^{(}-n))*(1-q^{(}-n)*q)*(1-q^{(}-n)*q^{2})*(1-a*b*q^{(}n+1))*(1-a*b*q^{(}n+1)*q)*(1-a*b*q^{(}n+1)*q^{2})*q^{3}*x^{3}/((1-a*q)*(1-a*q^{2})*(1-a*q^{3})*(1-q)*(1-q^{2})*(1-q^{3}))}
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
Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin