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

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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