功能:Completely symmetric integral of the second kind

格式:EllipticRG(x,y,z)

说明:本函数等于0.25*Int[((t+x)*(t+y)*(t+z))^(-0.5)*(x/(t+x)+y/(t+y)+z/(t+z))*t,t,0,∞],其中Int[((t+x)*(t+y)*(t+z))^(-0.5)*(x/(t+x)+y/(t+y)+z/(t+z))*t,t,0,∞]表示((t+x)*(t+y)*(t+z))^(-0.5)*(x/(t+x)+y/(t+y)+z/(t+z))*t函数对变量t从0到∞进行定积分.

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