小q雅可比多项式

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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].

pn(x;a,b;q)=2ϕ1(q−n,abqn+1;aq;q,xq)

例子

k=3,

p=1+q*x/((1−a*q)*(1−q))−q2*x*a*b*qn/((1−a*q)*(1−q))−q*x/((1−a*q)*(1−q)*qn)+q2*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)*q2*x2/((1−a*q)*(1−a*q2)*(1−q)*(1−q2)) +(1−q(−n))*(1−q(−n)*q)*(1−q(−n)*q2)*(1−a*b*q(n+1))*(1−a*b*q(n+1)*q)*(1−a*b*q(n+1)*q2)*q3*x3/((1−a*q)*(1−a*q2)*(1−a*q3)*(1−q)*(1−q2)*(1−q3))

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

参考文献

  1. ↑ Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin

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