help on integration

*To*: mathgroup at yoda.physics.unc.edu*Subject*: help on integration*From*: thomson_p at maths.su.oz.au (Peter Thomson)*Date*: Wed, 25 Nov 92 10:50:52 +1100

Dear Mathgroup, I have the following function that I wish to integrate over (0,q), In[1]:= f[q_]=(L^a/Gamma[a])^2 Exp[-L(c s-q^2)/(c-q)](q(s-q))^(a-1) 2 a -1 + a -1 + a L q (-q + s) Out[1]= ---------------------------------- 2 (L (-q + c s))/(c - q) 2 E Gamma[a] In[2]:= Integrate[f[q],{q,0,s}] Out[2]= Integrate[ 2 -(L c) - L q + (-(L c ) + L c s)/(-c + q) 2 a -1 + a -1 + a E L q (-q + s) > ----------------------------------------------------------------------, 2 Gamma[a] > {q, 0, s}] Mma not surprisingly cannot perform this integration directly. I was wondering if anyone can recognise this as being of a standard form that I can coerce Mma to perform. Any tips would be most appreciated. Incidentally, The application arose from the convolution of two gamma random variables (correlated, not independent). I noticed that the ContinuousDistributions.m Package uses an unusual definition of the parameter lambda which needs to be inverted to obtain the more usual definition for the density, i.e. In[3]:= <<DataAnalysis/ContinuousDistributions.m In[4]:= Density[GammaDistribution[alpha,1/lambda],t] alpha -1 + alpha lambda t Out[4]= ----------------------- lambda t E Gamma[alpha] Peter Thomson, School of Mathematics and Statistics, University of Sydney NSW 2006 Australia email: thomson_p at maths.su.oz.au