HP Prime: built-in inverse function of erf?

[Albert Chan]

(12-15-2023 01:06 PM)Gil Wrote:  Not quite so as I understood from Wikipedia, in article Error Function, Properties for Abs (z=a+ib) < 1 :

The inverse error function is usually defined with domain (−1,1), and it is restricted to this domain in many computer algebra systems. However, it can be extended to the disk |z| < 1 of the complex plane, using the Maclaurin series[9]

Then
Inv
ERF

(
(.8,-.2)
)
—>(.801172930851,-.341012371796)

Yes, we can define Maclaurin series solution as the "official" solution.
But, this is *not* properties of |z|<1. We still have infinite solutions.

> fsolve(erf(x)=0.8-0.2i, x=0.8-0.2i)  → 0.801172930852-0.341012371793*i
> fsolve(erf(x)=0.8-0.2i, x=1+3i)      → 1.53047592451+1.56695328912*i
> fsolve(erf(x)=0.8-0.2i, x=2+4i)      → 2.87803425787+3.00313505077*i
> fsolve(erf(x)=0.8-0.2i, x=3+5i)      → 3.7982932108+3.92873494629*i
> erf(Ans)                                        → 0.8-0.2i