erfi(::BigFloat)

[cossio]

julia> SpecialFunctions.erfi(big"1")
ERROR: MethodError: no method matching erfi(::BigFloat)

Since SpecialFunctions.erf works with BigFloat, I suspect that erfi could work too without much hassle?

[simonbyrne]

For erf we just call the MPFR function (https://www.mpfr.org/mpfr-current/mpfr.html#Special-Functions). It doesn't provide an erfi function, so we would have to write our own.

[cossio]

@simonbyrne One (probably inefficient) way of doing it is to rely on erf(::Complex{BigFloat}), which is already defined.

myerfi(x::BigFloat) = imag(erf(x*im))

[simonbyrne]

Ah, that's not good: it is just converting it to Complex{Float64}:
https://github.com/JuliaMath/SpecialFunctions.jl/blob/master/src/erf.jl#L27

We should change that.

[cossio]

new issue #119

[cossio]

Now that #119 is closed, perhaps we can add erfi(x::BigFloat) = imag(erf(x*im))?

[simonbyrne]

We could, but it will just throw a MethodError either way.

[simonbyrne]

(MPFR doesn't provide a complex erf function)

[flmuk]

any updates on this? a solution to this would be extremely handy

[stevengj]

Writing special functions is not easy — this would require a from-scratch implementation.

[flmuk]

I understand. Actually I only need $$erfi(x)$$ for real arguments, not complex ones. Is there a workaround for that? I guess I could write the Maclaurin series for that one, are there some pitfalls to avoid?

[stevengj]

A Taylor–Maclaurin series is generally a very slow way to compute special functions except in a small region of the domain. Usually people use a Taylor series near roots, and otherwise use things like continued-fraction expansions.