I also noticed that maxima cannot integrate gamma_incomplete(s, +-x^n) for n=1,2,3,4, etc. which Mathematica can do. I
hope that can be done too.
Rich
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From: "Dieter Kaiser" <drdieterkaiser at web.de>
Sent: Saturday, March 06, 2010 7:49 AM
To: "Richard Hennessy" <rich.hennessy at verizon.net>
Cc: "Maxima List" <maxima at math.utexas.edu>
Subject: Re: [Maxima] Integrating gamma_incomplete
> 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
>
>
>