Can imaginary Erf function be converted to regular Erf?

• To: mathgroup at smc.vnet.net
• Subject: [mg5839] Can imaginary Erf function be converted to regular Erf?
• From: Michael Hucka <hucka at eecs.umich.edu>
• Date: Tue, 28 Jan 1997 03:43:04 -0500
• Organization: University of Michigan EECS, Ann Arbor, Mich., USA
• Sender: owner-wri-mathgroup at wolfram.com

```I have a situation in which I get Erfi as part of an expression in
Mathematica 2.2.  However, I noticed that Erfi[z] *seems* to be real for real
z (this is just a trivial observation based on plugging in various values and
evaluating the result -- could be very wrong, I know).

Is there some conversion one can do to change the Erfi in this case (i.e.,
when z is known to be always real) to another form, say involving Erf or the
complementary Erf function?  I'd like to replace the Erfi somehow with
something real.  (I happen to know the result of my expression must be real.)

Just in case it's relevant, here's an example of the kind of expression I have:

2                             2
2       2        Sqrt[x ]             2        Sqrt[x ]
x  Sqrt[x ] Erfi[----------]   3 Sqrt[x ] Erfi[----------]
Sqrt[2] sx                    Sqrt[2] sx
Out[102]= ---------------------------- - ---------------------------
2      2                      2      2
x /(2 sx )              7     x /(2 sx )              5
E           Sqrt[2 Pi] sx     E           Sqrt[2 Pi] sx

sx is always positive real, and x is real and ranges from about -10 to +10.

--
Mike Hucka     hucka at umich.edu     <URL: http://ai.eecs.umich.edu/people/hucka>
PhD to be, computational models of human visual processing (AI Lab) University
UNIX systems administrator & programmer/analyst (EECS DCO)      of Michigan

```

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