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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
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