Integrate + Conjugate = Indeterminate

• To: mathgroup at smc.vnet.net
• Subject: [mg120651] Integrate + Conjugate = Indeterminate
• From: Sebastian Hofer <sebhofer at gmail.com>
• Date: Tue, 2 Aug 2011 07:12:15 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j0tru0\$d4m\$1@smc.vnet.net>

```I know that my question was originally posed in a very vague way, which was partly due to me having no idea where my problems came from. After more analysis of the involved expressions, I managed to get them into a form which can be evaluated numerically without getting Indeterminate values. What I essentially did was to use a combination of iterated Expands and replacement rules like

Expand[#] /. Power[E, x_] :> Power[E, FullSimplify@Expand@x]

(the expressions involve several similar exponentials which are multiplied and added...). Also, as the whole expression is the result of an integral, I separated the sub-expression which needed to be integrated before the integration and put everything back together afterwards.

Also, I was bitten by (let's call it) a very peculiar "feature" of Mathematica's handling of Conjugate:

In[25]:= Integrate[
Exp[(Sqrt[a + I b] - Conjugate[Sqrt[a - I b]]) x], {x, x0, x1},
Assumptions -> a > 0 && b > 0]

Out[25]= (-E^(
x0 (Sqrt[a + I b] - Conjugate[Sqrt[a - I b]])) + E^(
x1 (Sqrt[a + I b] - Conjugate[Sqrt[a - I b]])))/(Sqrt[a + I b] -
Conjugate[Sqrt[a - I b]])

In[23]:= Out[18] /. {a -> 1, b -> 2} // N

During evaluation of (Local 2) In[23]:= Power::infy: Infinite expression 1/(0. +0. I)
encountered. >>

During evaluation of (Local 2) In[23]:= Power::infy: Infinite expression 1/(0. +0. I)^1.
encountered. >>

During evaluation of (Local 2) In[23]:= Infinity::indet: Indeterminate expression (0. +0. I) ComplexInfinity
encountered. >>

Out[23]= Indeterminate

Of course this holds for all a,b. Is there any logical explanation for this? Or better: Is there a way to get around it? This problem is probably known to many of you, but it was new to me and I would think it is a bug...

Sebastian

```

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