topic How to enter imaginary error function (erfi) in formula column in Discussions

How to enter imaginary error function (erfi) in formula column

ansouk — Sat, 10 Jun 2023 20:54:53 GMT

I have a strong indication my data follow imaginary error function (erfi) function <https://en.wikipedia.org/wiki/Error_function>. Please recommend a way to input erfi into a formula column to be used in nonlinear fit platform. Both the argument and the function are real, so there is no need to use imaginary or complex numbers here. The plot looks very similar to one here Erfi—Wolfram Language Documentation . The derivative looks like a parabola in semi-log coordinates, but it is very noisy, so I have to fit the integral, which calls for erfi in the column formula.

Re: How to enter imaginary error function (erfi) in formula column

MRB3855 — Tue, 18 Apr 2023 08:22:12 GMT

As it says in the wiki link you sent, "In statistics, for non-negative values of x, the error function has the following interpretation: for a random variable Y that is normally distributed with mean 0 and standard deviation 1/√2, erf x is the probability that Y falls in the range [−x, x].". So, a little algebra etc gives you erf(x) = the following in JMP:

Re: How to enter imaginary error function (erfi) in formula column

ansouk — Tue, 25 Apr 2023 17:32:54 GMT

I asked about erfi, and you answered about erf. Those are very different functions. I need a solution for erfi.

Re: How to enter imaginary error function (erfi) in formula column

ansouk — Tue, 25 Apr 2023 19:36:24 GMT

I guess I can use series approximation of erfi: Series[Erfi[x], {x, 0, 8}] - Wolfram|Alpha (wolframalpha.com) Can you think of something better?

Re: How to enter imaginary error function (erfi) in formula column

MRB3855 — Wed, 26 Apr 2023 10:11:52 GMT

Oops my bad...wrong error function! Yes, a series approximation looks like your best bet.