HP Prime: built-in inverse function of erf?

[Albert Chan]

Hi, Gil

I think erf inverse function is defined only for real x within ±1, otherwise we get infinite solutions.

> fsolve(erf(x)=2, x=i)            → 0.869417565326+1.34059481853*i
> fsolve(erf(x)=2, x=1+3i)      → 1.88472598633+2.28183639616*i
> fsolve(erf(x)=2, x=2+4i)      → 2.55833225411+2.9104037265*i
> fsolve(erf(x)=2, x=3+5i)      → 3.55858803599+3.85919595309*i

> fsolve(erf(x)=i, x=i)            → 0.731697153468*i
> fsolve(erf(x)=i, x=1+3i)      → 1.52285714842+2.04084734052*i
> fsolve(erf(x)=i, x=2+4i)      → 2.87881932565+3.2674470432*i
> fsolve(erf(x)=i, x=3+5i)      → 3.79852906513+4.13183559565*i

erf(z) = 2 --> erf(conj(z)) = conj(2) = 2-0i      → erfinv(2+0i) ≠ erfinv(2-0i)
erf(z) = i --> erf(-conj(z)) = -conj(i) = -0+i      → erfinv(0+i) ≠ erfinv(-0+i)

If we don't care about ±0, we doubled solutions for both erfinv(2) and erfinv(i)