Re: Solving a Integral

• To: mathgroup at smc.vnet.net
• Subject: [mg78125] Re: Solving a Integral
• From: dimitris <dimmechan at yahoo.com>
• Date: Sat, 23 Jun 2007 07:14:20 -0400 (EDT)
• References: <f5dkds\$no\$1@smc.vnet.net>

```I think tour integral
does not have a closed form
solution (at least using Mathematica
for evaluating!).

Did you search some of the well known
collections of integral tables?

Dimitris

ehrnsperge... at pg.com       :
> I need help in solving the following integral:
>
> Integral = 1/(beta^alpha* Gamma[alpha]) *
> Integrate[x^(alpha-1)*Exp[-x/beta]/(1+Exp[-a*x-b]),{x,0, infinity},
> Assumptions: (alpha> 0)||(beta > 0)||(a > 0)||(b <0)]
>
> The Integral is approximately 1/(beta^alpha* Gamma[alpha])
> *1/(1+Exp[-a*alpha*beta-b]) + Order[alpha*beta^2]
>
> However, I would like to have an exact analytical solution, and I am
> failing to convince Mathematica to give me the solution. Is there a way to
> ask Mathematica to give the solution as a series expansion of my
> approximate solution?
>
> Thanks so much for your help,
>
> Bruno
>
> Dr. Bruno Ehrnsperger
> Principal Scientist
>
> Procter & Gamble Service GmbH
> Sulzbacherstr.40
> 65824 Schwalbach
> Germany
>
> fon +49-6196-89-4412
> fax +49-6196-89-22965
> e-mail: ehrnsperger.b at pg.com
> internet: www.pg.com
>
> Gesch=E4ftsf=FChrer: Otmar W. Debald, Gerhard Ritter, Dr. Klaus Schumann,
> Willi Schwerdtle
> Sitz: Sulzbacher Str. 40, 65824 Schwalbach am Taunus, Amtsgericht:
> K=F6nigstein im Taunus HRB 4990

```

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