连续双哈恩多项式

连续双哈恩多项式(Continuous dual Hahn polynomials)是一个正交多项式，由下列广义超几何函数定义^[1]

${\displaystyle S_{n}(x^{2};a,b,c)={}_{3}F_{2}(-n,a+ix,a-ix;a+b,a+c;1).\ }$

连续双哈恩多项式

连续双哈恩多项式 复数图

${\displaystyle {\begin{aligned}R1&=(a+2.3)*(a+3.5)*hypergeom([-1,a+I*x,a-I*x],[a+2.3,a+3.5],1)\\R2&=pochhammer(a+2.3,2)*pochhammer(a+3.5,2)*hypergeom([-2,a+I*x,a-I*x],[a+2.3,a+3.5],1)\\R3&=pochhammer(a+2.3,3)*pochhammer(a+3.5,3)*hypergeom([-3,a+I*x,a-I*x],[a+2.3,a+3.5],1).\end{aligned}}}$