I have finished some further work to integrate the Unit Step function and
general sums. A lot of integrals with the Unit Step function including general
sums with the Unit Step function now give nice and correct results. Two examples
with the new algorithm are:
(%i10) radcan(specint(%e^-(s*t)*sum(unit_step(t-n*k),n,0,inf),t)),simpsum;
(%o10) %e^(k*s)/(s*%e^(k*s)-s)
(%i11)
radcan(specint(%e^-(s*t)*sum(a^(n-1)*unit_step(t-n*k),n,1,inf),t)),simpsum;
(%o11) 1/(s*%e^(k*s)-a*s)
A&S gives 129 integrals. Now $SPECINT gives for 100 integrals a correct result
and for 29 integrals a correct noun form.
Most of the integrals $SPECINT can't evaluate include the argument 1/sqrt(t) for
the Erf function and the argument sqrt(t^2-k^2) for the Bessel functions.
Furthermore some integrals with Exponential Integrals $SPECINT can't evaluate.
Because I work on a completly different file with a lot of extra modifications I
started to collect all changes and extensions to the code in the original file
hypgeo.lisp.
Dieter Kaiser