查看“︁小q雅可比多项式”︁的源代码



'''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<ref>Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin</ref>.

:<math>\displaystyle  p_n(x;a,b;q) = {}_2\phi_1(q^{-n},abq^{n+1};aq;q,xq)  </math>

==例子==
k=3,

<math>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))</math>
<math>(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))</math>
<math>+(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))</math>

==图集==
{|
|[[File:LITTLE Q-JACOBI POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT.gif|thumb|LITTLE Q-JACOBI POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT]]
|[[File:LITTLE Q-JACOBI POLYNOMIALS IM COMPLEX 3D MAPLE PLOT.gif|thumb|LITTLE Q-JACOBI POLYNOMIALS IM COMPLEX 3D MAPLE PLOT]]
|[[File:LITTLE Q-JACOBI POLYNOMIALS RE COMPLEX 3D MAPLE PLOT.gif|thumb|LITTLE Q-JACOBI POLYNOMIALS RE COMPLEX 3D MAPLE PLOT]]
|}
{|
|[[File:LITTLE Q-JACOBI POLYNOMIALS ABS DENSITY MAPLE PLOT.gif|thumb|LITTLE Q-JACOBI POLYNOMIALS ABS DENSITY MAPLE PLOT]]
|[[File:LITTLE Q-JACOBI POLYNOMIALS IM DENSITY MAPLE PLOT.gif|thumb|LITTLE Q-JACOBI POLYNOMIALS IM DENSITY MAPLE PLOT]]
|[[File:LITTLE Q-JACOBI POLYNOMIALS RE DENSITY MAPLE PLOT.gif|thumb|LITTLE Q-JACOBI POLYNOMIALS RE DENSITY MAPLE PLOT]]
|}

==参考文献==
<references/>

[[Category:正交多项式]]
[[Category:基本超几何函数]]
{{q超几何函数}}