﻿功能:Completely symmetric integral of the second kind

格式:EllipticRG(x,y,z)

说明:
$$
\begin{aligned}
\mathbf{EllipticRG}(x, y, z) &= \dfrac{1}{4}\int_0^\infty (\dfrac{tx}{t + x} + \dfrac{ty}{t + y} + \dfrac{tz}{t + z})\dfrac{1}{\sqrt{(t + x)(t + y)(t + z)}}dt
\\
\\
\mathbf{s}\cdot\mathbf{t}\cdot&:x\geq 0,y\geq 0,z\geq 0
\end{aligned}
$$

注意:EllipticRG(x,y,z)=0.5*(z*{EllipticRF<算式解析\EllipticRF>}(x,y,z)-(x-z)*(y-z)*{EllipticRD<算式解析\EllipticRD>}(x,y,z)/3+(x*y/z)^0.5)

参考:《NUMERICAL COMPUTATION OF REAL OR COMPLEX ELLIPTIC INTEGRALS》_B.C.CarlsonAmes_Laboratory and Department of Mathematics, Iowa State University,Ames, Iowa 50011-3020, USA

例子:

EllipticRG(i,i,i)//回车得到如下结果
ans = 0.707106781186547 + 0.707106781186547i