说明：  泽尼克多项式的阶数 for n=0:k for m=0:n if j>=kj break;end if mod(n-m,2)==0 Rnm=0; for s=0:(n-m)/2 fenmu=factorial(s)*factorial((n+m)/2-s)*factorial((n-m)/2-s); Rnm=Rnm+(-1)^s*r^(n-2*s)*factorial(n-s)/fenmu; end if m==0 Zj(1,j)=sqrt(n+1)*Rnm; mnj(1,j)=n+i*m; j=j+1; elseif mod(j,2)==0 Zj(1,j)=sqrt(2*n+2)*Rnm*cos(m*sita); Zj(1,j+1)=sqrt(2*n+2)*Rnm*sin(m*sita); mnj(1,j)=n+i*m; mnj(1,j+1)=n+i*m; j=j+2; else Zj(1,j)=sqrt(2*n+2)*Rnm*sin(m*sita); Zj(1,j+1)=sqrt(2*n+2)*Rnm*cos(m*sita); mnj(1,j)=n+i*m; mnj(1,j+1)=n+i*m; j=j+2; end end end end
(for n=0:k for m=0:n if j>=kj break;end if mod(n-m,2)==0 Rnm=0; for s=0:(n-m)/2 fenmu=factorial(s)*factorial((n+m)/2-s)*factorial((n-m)/2-s); Rnm=Rnm+(-1)^s*r^(n-2*s)*factorial(n-s)/fenmu; end if m==0 Zj(1,j)=sqrt(n+1)*Rnm; mnj(1,j)=n+i*m; j=j+1; elseif mod(j,2)==0 Zj(1,j)=sqrt(2*n+2)*Rnm*cos(m*sita); Zj(1,j+1)=sqrt(2*n+2)*Rnm*sin(m*sita); mnj(1,j)=n+i*m; mnj(1,j+1)=n+i*m; j=j+2; else Zj(1,j)=sqrt(2*n+2)*Rnm*sin(m*sita); Zj(1,j+1)=sqrt(2*n+2)*Rnm*cos(m*sita); mnj(1,j)=n+i*m; mnj(1,j+1)=n+i*m; j=j+2; end end end end)