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
参考文献
编辑
^ Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin
