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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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