Your change of variable converts the lower limit of integration to either -infinity for infinity
(depending on the sign of B). The function changevar doesn't handle such things correctly, I think.
You could try changing the lower limit to a new symbol---I wasn't able to push this any further.
For integer N, one thing that might work:
(%i1) assume(C>0, B>0);
(%o1) [C>0,B>0]
(%i2) marginal : integrate((1/t-C)^(N-1)*exp(A-B/t^2),t,0,1/C);
(%o2) integrate(%e^(A-B/t^2)*(1/t-C)^(N-1),t,0,1/C)
(%i3) makelist(ev(marginal, N : k, integrate),k,1,3);
(%o3) [(gamma_incomplete(-1/2,B*C^2)*%e^A*sqrt(B))/2,-(gamma_incomplete(-1/2,B*C^2)*%e^A*sqrt(B)*C-gamma_incomplete(0,B*C^2)*%e^A)/2,-(-gamma_incomplete(-1/2,B*C^2)*%e^A*B*C^2+2*gamma_incomplete(0,B*C^2)*%e^A*sqrt(B)*C-gamma_incomplete(1/2,B*C^2)*%e^A)/(2*sqrt(B))]
--Barton
-----maxima-bounces at math.utexas.edu wrote: -----
To: Maxima mailing list <maxima at math.utexas.edu>
From: Dan
Sent by: maxima-bounces at math.utexas.edu
Date: 01/22/2012 03:08PM
Subject: Integrating a Gaussian wrt its width
Dear All,
I'm interested in integrals of the form:
declare(N,integer) ;
assume(N > 0) ;
assume(N > 1) ;
marginal : 'integrate((1/t-C)^(N-1)*exp(A-B/t^2),t,0,1/C) ;
Inspired by Jeffreys (1961, _Theory of Probability_, Oxford University
Press, p. 139), I thought a nice way forward would be to reduce this
to a finite series of incomplete Gamma functions, using the
substitution
changevar(marginal,u+B/t^2,u,t) ;
but all I get when I issue this changevar command is the error
sign: sign of infinity is undefined.
??-- an error. To debug this try: debugmode(true);
Any ideas, please?
--
Thanks,
Dan
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