erfi function

Imaginary error function (could be complex) using matlab's incomplete gamma function gammainc

Description

Imaginary error function, as it is defined in Mathematica erfi(z)==erf(iz)/i (z could be complex) using the incomplete gamma function in matlab: gammainc

• MATLAB release: MATLAB 7 (R14)

[Ian]

-Good work with this function Per!!
-While preforming an optimisation using this function. A bug in MATLAB 7.10 (R2010a) was reported. The function enters an infinite loop when calling gamminc(x,a) with x<0 and abs(x)>>a. They are working to fix this in future releases.
kind regards,
Ian Gregory, Sydney.

[kinor]

Hi Ian,

thank your for the hint

and you of course for sharing the function Per!

best

kinor

[PLH]

 

[PLH]

The program does not work as stated. When using complex z (i.e., not pure real, or pure imaginary), I get the following error:

Error using ==> gammainc
Inputs must be real, full, and double or single.

Error in ==> erfi at 19
ans=~isreal(x).*(-(sqrt(-x.^2)./(x+isreal(x))).*gammainc(-x.^2,1/2))+...

This also occurs for Example 2 provided with the code. I'm assuming it's a trivial problem since the figure above seems to correspond to what I would expect (look at the erfi article on Mathworld ). In case it's relevant, I'm using Matlab 7.10.0.499 (R2010a) (64-bit).

[Marcelo Pisani]

Function gives wrong results for high moduli input. For instance, using Maple ERF converted to DOUBLE (erfz2 function below):

>> z=3+2i; erfz2(z*i)/i, erfi(z)
ans =
   8.6873 -20.8295i
ans =
   8.6873 -20.8295i

>> z=7+7i; erfz2(z*i)/i, erfi(z)
ans =
  -0.0561 + 1.0102i
ans =
  7.3774e+024 +1.6269e+025i

[Mohamed Yassin OUKILA]

what is erfz2?