the problem

• To: mathgroup at yoda.physics.unc.edu
• Subject: the problem
• From: ECORTES at indyvax.iupui.edu
• Date: Wed, 29 Sep 1993 14:36:17 -0500

```I have two algebraic coupled equations for two complex parameters a and b.
In the first equation I have the integral over x (real) from 0 to 1 of the
function: x/(a^2+b^2) and we have this integral equal to a given complex
constant u; in the second equation I have the integral over x (real) from 0
to 1 of the function x Exp[-b/x]/(ax+b) and we have this integral equal to
another given complex constant v. (We need the restriction Re[b]>0.)
Now I have two difficulties in handling this kind of problem with
Mathematica, and of course I have to deal with some more complicated
expressions, but this example gives the idea:
1) The first difficulty is that if I use the command ComplexExpand to
rationalize each integrand and separate the real and imaginary parts for
each integration, it gives me in the denominator the expression:
Abs[ of a complex quatity]
without evaluating it explicitly, and this is because the argument is not
numerical. I would need the complete algebraic separation in order to do
each integration.
2) The other problem is the next step, which is how to solve the system of
4 coupled equations for the real parameters:
Re[a], Im[a], Re[b] and Im[b].
If we define the first integration as Y1 and the second as Y2, is it
possible to use the command
FindRoot[{Re[Y1]==Re[u], Im[Y1]==Im[u], Re[Y2]==Re[v], Im[Y2]==Im[v],
{Re[a], a10}, {Im[a], a20}, {Re[b],b10}, {Im[b],b20}]?

If this idea is not clear enough, I could send a letter with the equations
and other comments to the Math Group.
Emilio Cortes

--Boundary (ID pzvat0CSAlpCGSqTarvSfg)--

```

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