Taylor expansions are contagious. When maxima multiplies exp(-x^2/4)
times a
Taylor polynomial, the product gets expanded as a Taylor polynomial. To
do the calculation, use 'ratsimp' to convert from a Taylor polynomial to
a non-taylor.
Also, I think you want 'minf and 'inf instead of %minf and %inf.
(%i3) kill(all)$
(%i1) f(x):=x-2*log((exp(x)+1)/2) + x**2/4$
(%i2) exp(-x**2/4)*ratsimp(taylor(exp(f(x))*(x*kb+mu)**gamma,x,0,4))$
(%i3) display2d : false$
(%i4) integrate(%o2,x,'minf,'inf)/4;
Is gamma+4 positive, negative, or zero?
pos;Is mu positive or negative?
pos;Is gamma an integer?
no;Is gamma+3 positive, negative, or zero?
pos;Is kb*gamma positive, negative, or zero?
pos;Is gamma+2 positive, negative, or zero?
pos;Is kb^2*gamma positive, negative, or zero?
pos;Is gamma+1 positive, negative, or zero?
pos;Is gamma positive, negative, or zero?
pos;Is kb zero or nonzero?
nonzero;Is kb positive or negative?
pos;(%o4) (24*sqrt(%pi)
*(8*kb^4*mu^gamma*gamma^4-48*kb^4*mu^gamma*gamma^3
+88*kb^4*mu^gamma*gamma^2
-48*kb^4*mu^gamma*gamma+2*mu^(gamma+4))
+4*sqrt(%pi)*(96*kb^2*mu^(gamma+2)*gamma^2-96*kb^2*mu^(gamma+2)*gamma)
+384*sqrt(%pi)*mu^(gamma+4))
/(768*mu^4)
Barton
David Ronis
Sent by: maxima-admin@math.utexas.edu
02/01/2005 11:52 AM
Please respond to david.ronis
To: maxima@math.utexas.edu
cc:
Subject: [Maxima] Bug in today's CVS
I'm trying to use maxima to do a saddle point integration with the
following:
f(x):=x-2*log((exp(x)+1)/2) + x**2/4;
exp(-x**2/4)*taylor(exp(f(x))*(x*kb+mu)**gamma,x,0,4);
integrate(%,x,%minf,%inf)/4;
As far as I can tell, the taylor expansion is done correctly, however,
the multiplication by the additional exponential in the second line
seems to be ignored. The resulting integral doesn't converge and I'm
left with explicit %inf/%minf's at the integration (which is wrong in
any event).
David
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