Re: Integrate[E^x/Cos[x]]
- To: mathgroup at smc.vnet.net
- Subject: [mg38015] Re: Integrate[E^x/Cos[x]]
- From: Hendrik van Hees <hees at physik.uni-bielefeld.de>
- Date: Tue, 26 Nov 2002 00:48:36 -0500 (EST)
- References: <arsip9$een$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Peter Breitfeld wrote:
> I want to evaluate the integral:
>
> f[u_] = Integrate[E^x/Cos[x], {x, 0, u},
> Assumptions -> {x \[Element] Reals, u < Pi/2}]
>
> Mathematica 4.2 on Linux returns
>
> (1 - I)*E^((1 + I)*u)*Hypergeometric2F1[
> 1/2 - I/2, 1, 3/2 - I/2, -E^(2*I*u)] +
> (1/2)*((-I)*PolyGamma[0, 1/4 - I/4] +
> I*PolyGamma[0, 3/4 - I/4])
>
> so far so good. This integral should be real-valued, at least in the
> Range 0<=u<Pi/2. And that is my problem. How can I get a real result
> with no imaginary I's. Neither FunctionExpand or FullSimplify did it.
As far as I can see the imaginary parts of the numerical evaluation of the
above expression are numerical artifacts. They are around <10^(-15). So you
should use Chop[f[u]] to suppress these numerical uncertainties.
--
Hendrik van Hees Fakultät für Physik
Phone: +49 521/106-6221 Universität Bielefeld
Fax: +49 521/106-2961 Universitätsstraße
http://theory.gsi.de/~vanhees/ D-33615 Bielefeld