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MathGroup Archive 2007

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DIfference of error functions with complex arguments

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77145] DIfference of error functions with complex arguments
  • From: Ale <theopps75 at yahoo.it>
  • Date: Tue, 5 Jun 2007 06:26:58 -0400 (EDT)

Hi... I am studing the harmonic responce of a photophysical system.
After a convolutio, part the solution contains:

\!\(Erf[\(\((\(-1\))\)\^\(1/4\)\ \((a + 2\ \@t\ \((1 - \[ImaginaryI]\
=CF=86)\))\)\
\)\/\(2\ \@\(\[ImaginaryI] + =CF=86\)\)] - Erf[\(\((\(-1\))\)\^\(1/4\)\ a\)
\/\(2\ \
\@\(\[ImaginaryI] + =CF=86\)\)]\)

That is the difference between two error functions of complex
argument.

Knowing that the following assumptions can be used:

Assumptions -> {a > 0, =CF=86 > 0, t > 0, a =CF=86 t =E2=88=88 Reals}

Can I somehow obtain this part of equation in the form Ro Exp [-i
Phi] ?


More in general, if one have Erf[x]+Erf[y], with x and y complex
numbers, is it possible to express analytically the module and
argument of the sum?

Thanks

Alessandro



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