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 > >