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MathGroup Archive 2007

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Re: DIfference of error functions with complex arguments

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77236] Re: DIfference of error functions with complex arguments
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 6 Jun 2007 06:48:53 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <f43dvq$jo$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

look at Abramowitz/Stegun Pocketbook of mathematical funtions
formula 7.1.29

or

http://functions.wolfram.com/GammaBetaErf/Erf/19/01/

Re[Erf[x + I y]] == (1/2) (Erf[x - x Sqrt[-(y^2/x^2)]] + Erf[x + x 
Sqrt[-(y^2/x^2)]])

http://functions.wolfram.com/GammaBetaErf/Erf/19/02/

Im[Erf[x + I y]] == (x/(2 y)) Sqrt[-(y^2/x^2)] (Erf[x - x 
Sqrt[-(y^2/x^2)]] - Erf[x + x Sqrt[-(y^2/x^2)]])

to split the real and imaginary part of your Erf[x+I*y]+Erf[u+I*v] 
expression

Regards
   Jens

Ale wrote:
> 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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