Well, it WAS working. I seem to have messed it up. It does not work anymore. I don't know what I did to it wrong, but
it was working. Could someone help?
Rich
--------------------------------------------------
From: "Richard Hennessy" <rich.hennessy at verizon.net>
Sent: Monday, March 08, 2010 6:26 PM
To: "Dieter Kaiser" <drdieterkaiser at web.de>
Cc: "Maxima List" <maxima at math.utexas.edu>
Subject: Re: [Maxima] Integrating gamma_incomplete
> Hi Dieter,
>
> I came up with this gm.mac file.
>
> /* gm.mac */
> matchdeclare([a,s],freeof(x),x,true,[m,n],nonnegintegerp)$
> block(
> [simp:false],
> tellsimp('integrate(gamma_incomplete(s, a*x^n), x),x*gamma_incomplete(s, a*x^n) - (x*gamma_incomplete(1/n + s,
> a*x^n))/(a*x^n)^(1/n)),
> tellsimp('integrate(gamma_incomplete(s, a*x^n)*x^m, x),x*gamma_incomplete(s, a*x^n)*x^m/(m+1)
> - (x*gamma_incomplete((m+1)/n + s, a*x^n))/((m+1)*a^(m+1)*(x^n)^(1/n)))
> )$
> remove([a,s,x,m,n],matchdeclare)$
> declare(integrate,linear);
> assume(x>0);
> /* eof */
>
> If you load this then you can do any (repeated any number of times or just once) integral of x^n*gamma_incomplete(s,
> b*x^m) where n and m are nonnegative integers and b is positive. I personally don't know if x<0 has meaning or
> usefulness in the applications. So this is good enough for me. It would be nice if Maxima could do this without this
> file. I verified the results with diff and they seem to be right.
>
> HTH,
>
> Rich
>
>
> --------------------------------------------------
> 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
>>
>>
>>
>
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