>>939
検証
α2ω=\(α){
x=Re(α)
y=Im(α)
ω1=x*((-x*(x/(x^2+y^2))-y*(-y/(x^2+y^2))+(x/(x^2+y^2))^2+(-y/(x^2+y^2))^2)/(x^2-2*x*(x/(x^2+y^2))+y^2-2*y*(-y/(x^2+y^2))+(x/(x^2+y^2))^2+(-y/(x^2+y^2))^2))+
x/(x^2+y^2)*(1- ((-x*(x/(x^2+y^2))-y*(-y/(x^2+y^2))+(x/(x^2+y^2))^2+(-y/(x^2+y^2))^2)/(x^2-2*x*(x/(x^2+y^2))+y^2-2*y*(-y/(x^2+y^2))+(x/(x^2+y^2))^2+(-y/(x^2+y^2))^2)))
ω2=y*((-x*(x/(x^2+y^2))-y*(-y/(x^2+y^2))+(x/(x^2+y^2))^2+(-y/(x^2+y^2))^2)/(x^2-2*x*(x/(x^2+y^2))+y^2-2*y*(-y/(x^2+y^2))+(x/(x^2+y^2))^2+(-y/(x^2+y^2))^2))+
(-y/(x^2+y^2))*(1- ((-x*(x/(x^2+y^2))-y*(-y/(x^2+y^2))+(x/(x^2+y^2))^2+(-y/(x^2+y^2))^2)/(x^2-2*x*(x/(x^2+y^2))+y^2-2*y*(-y/(x^2+y^2))+(x/(x^2+y^2))^2+(-y/(x^2+y^2))^2)))
ω1 + 1i*ω2
}

A2H = \(a,b) (a+b*1i) + (2*a*b*1i)/((a^2+b^2)*((a-b*1i)-1/(a-b*1i)))

α2ω(1+2i) ; A2H(1,2)
α2ω(-1+1i) ; A2H(-1,1)
α2ω(1+1i) ; A2H(1,1)

> α2ω(1+2i) ; A2H(1,2)
[1] 0.3-0.1i
[1] 0.7+2.1i
> α2ω(-1+1i) ; A2H(-1,1)
[1] -0.6-0.2i
[1] -0.4+1.2i
> α2ω(1+2i) ; A2H(1,2)
[1] 0.3-0.1i
[1] 0.7+2.1i
> α2ω(-1+1i) ; A2H(-1,1)
[1] -0.6-0.2i
[1] -0.4+1.2i
> α2ω(1+1i) ; A2H(1,1)
[1] 0.6-0.2i
[1] 0.4+1.2i
合致せず。