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] 连续双哈恩多项式 连续双哈恩多项式 复数图 S n ( x 2 ; a , b , c ) = 3 F 2 ( − n , a + i x , a − i x ; a + b , a + c ; 1 ) . {\displaystyle S_{n}(x^{2};a,b,c)={}_{3}F_{2}(-n,a+ix,a-ix;a+b,a+c;1).\ } R 1 = ( a + 2.3 ) ∗ ( a + 3.5 ) ∗ h y p e r g e o m ( [ − 1 , a + I ∗ x , a − I ∗ x ] , [ a + 2.3 , a + 3.5 ] , 1 ) R 2 = p o c h h a m m e r ( a + 2.3 , 2 ) ∗ p o c h h a m m e r ( a + 3.5 , 2 ) ∗ h y p e r g e o m ( [ − 2 , a + I ∗ x , a − I ∗ x ] , [ a + 2.3 , a + 3.5 ] , 1 ) R 3 = p o c h h a m m e r ( a + 2.3 , 3 ) ∗ p o c h h a m m e r ( a + 3.5 , 3 ) ∗ h y p e r g e o m ( [ − 3 , a + I ∗ x , a − I ∗ x ] , [ a + 2.3 , a + 3.5 ] , 1 ) . {\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}}} 参考文献 ^ Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, doi:10.1007/978-3-642-05014-5, ISBN 978-3-642-05013-8, MR 2656096
![{\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}}}](/media/math_img/2041/c7e6b04ca8316d89d10932f6ca6ef11660bb8235.svg)
