Solving a Integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg78043] Solving a Integral*From*: ehrnsperger.b at pg.com*Date*: Thu, 21 Jun 2007 06:03:03 -0400 (EDT)

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