Am Freitag, den 05.03.2010, 22:07 -0500 schrieb Richard Hennessy:
> I noticed Maxima can only integrate gamma_incomplete a couple times.
> Mathematica can do it as many times as you want. Is this a weakness
> in integrate()?
Maxima can only integrate the direct function gamma_incomplete, but not
the case when a power is involved. Therefore, we get:
(%i2) integrate(gamma_incomplete(a,x),x);
(%o2) gamma_incomplete(a,x)*x-gamma_incomplete(a+1,x)
We get a noun form, when we repeat the integration:
(%i3) integrate(%,x);
(%o3) 'integrate(gamma_incomplete(a,x)*x,x)
-gamma_incomplete(a+1,x)*x+gamma_incomplete(a+2,x)
I have already proposed an extension on the mailing list
http://www.math.utexas.edu/pipermail/maxima/2010/020534.html to add the
integrals of the type x^v*gamma_incomplete(a,x). With this extension we
will get:
(%i5) integrate(gamma_incomplete(a,x),x);
(%o5) gamma_incomplete(a,x)*x-gamma_incomplete(a+1,x)
(%i6) integrate(%,x);
(%o6) (gamma_incomplete(a,x)*x^2-gamma_incomplete(a+2,x))/2
-gamma_incomplete(a+1,x)*x+gamma_incomplete(a+2,x)
(%i7) integrate(%,x);
(%o7) ((gamma_incomplete(a,x)*x^3-gamma_incomplete(a+3,x))/3
-gamma_incomplete(a+2,x)*x+gamma_incomplete(a+3,x))
/2
-(gamma_incomplete(a+1,x)*x^2-gamma_incomplete(a+3,x))/2
+gamma_incomplete(a+2,x)*x-gamma_incomplete(a+3,x)
All integrals are solved by Maxima.
Dieter Kaiser