I have put this on my site (gm.mac) and also added the special case below.
intgamma(gamma_incomplete(b, a*x)/x, x);
-> -%e^-(a*x)*(a^b*gamma(1-b)*x^(2*b)*log(a*x)-a^b*psi[0](1-b)*gamma(1-b)*x^(2*b)
+(-a*log(a)*expintegral_e(b,a*x)-a*hypergeometric_regularized([1-b,
1-b],[2-b, 2-b],-a*x)*gamma(1-b)^2)*x^(b+1))
Unfortunately I don't know how to eliminate the hypergeometric_regularized() function from the answer assuming that is
possible. This is a symbolic solution. Maxima as far as I know cannot evaluate the hypergeometic_regularized function.
You also cannot diff the answer to see if you get the original problem back. Anyway I guess it is right. I took a
limit of an expression involving expintegral_e() to get this answer (which Maxima can do). So this is the output from
the limit() function.
Rich
From: Richard Hennessy
Sent: Tuesday, March 16, 2010 2:21 AM
To: Maxima List
Subject: Dammar Incomplete integrator
Forgot the year.
Rich
_______________________________________________
Maxima mailing list
Maxima at math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima