The function specint (Laplace transform) can do this:
(%i37) p: fullratsimp(c*f/pdenom);
(%o37) (c^a*s^(-a-1)*%e^(-c/s))/(a*gamma(a))
(%i38) specint(%,c);
(%o38) gamma(a+1)/(a*gamma(a))
To view the user documentation for specint, enter "? specint". Maxima automatically simplifies a^(s) * a^(-s) to 1, but it seems that
Maple does not. Why integrate doesn't automatically dispatch specint is a mystery.
Welcome to Maxima
--Barton
________________________________________
From: maxima-bounces at math.utexas.edu [maxima-bounces at math.utexas.edu] on behalf of Lindsay Keegan [keeganlt at mcmaster.ca]
Sent: Monday, June 11, 2012 14:04
To: maxima at math.utexas.edu
Subject: Integrals
When I try to do the following integral:
assume(a>1);
declare(a, noninteger);
assume(s>0);
assume(H>0);
f: c^(a-1)/s^a*(exp(-c/s))/gamma(a);
pdenom: minfactorial(makefact(fullratsimp(integrate(c*f, c, 0, inf))));
p: fullratsimp(c*f/pdenom);
integrate(c*p*H/(c+H), c, 0, inf);
I get
(%i13) integrate(-----, c, 0, inf)
H + c
inf
/ a + 1 - c/s
- a - 1 [ c %e
s H I -------------- dc
] H + c
/
0
(%o13) ---------------------------------
a gamma(a)
However, when I do it in Maple it works and I get:
g0 := int(gd, x=0..infinity);
GAMMA(a~)
g0 := ----------------------
a~ (-a~)
s~ gamma(a~) s~
How can I get Maxima to do the integral?
Thank you,
Lindsay
Lindsay Keegan
PhD Candidate
Theoretical Biology Lab
Department of Biology
McMaster University
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