Challenging Integration
- To: mathgroup at smc.vnet.net
- Subject: [mg12747] Challenging Integration
- From: quartier at umnw.ethz.ch (Robin Quartier)
- Date: Wed, 10 Jun 1998 03:04:10 -0400
- Organization: ETH Zurich
- Sender: owner-wri-mathgroup at wolfram.com
Good Morning everybody. I have the following distribution: epsilon[x_]:=(a*b/(b^2 - a^2))*(b*Exp[-a*x] - a*Exp[-b*x]) a,b >0 This function is kind of symmetric, in the sens that it is stable for the permutation of a and b. It is a distribution, normalised on the positive half-axis The integration I want to make is: Integrate[epsilon[x]*Log[epsilon[x]],{x,0,Infinity}] Mathematica does not want to do it. I can get a primitive, Integrate[epsilon[x]*Log[epsilon[x]],x] But I don't think that the output I get is correct, because it is not symmetricalfor the permutation of a and b anymore. Namely, it contains an Hypergeometric function that diverges for a>b, and converges for a<b, which can not be. Ideas, questions and comments welcomed! Best regards Robin Quartier