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## RE: [Axiom-math] special functions

 From: Bill Page Subject: RE: [Axiom-math] special functions Date: Sun, 29 Jan 2006 18:44:22 -0500

```Yigal,

On January 28, 2006 9:31 AM I wrote:
>
> I am a rush right now, but I will get back to you later
> today. I think you have made a very good start.
>

http://wiki.axiom-developer.org/SandBoxGamma

This implements exactly the algorithm of Recipes eq. (6.27)
It uses a good numerical method (Lentz) for evaluating the
continued fraction.

I would like to talk to you so more about your use of Axiom's
ContinuedFraction domain. I think this is interesting for a
very different reason than just evaluating the incomplete
Gamma function. Continued fractions (especially as implemented
here in Axiom as "infinite" streams) is one of the better
methods for implement **exact** real arithmetic. But maybe
that is a subject for another day.

Regards,
Bill Page.

>
> On January 28, 2006 3:18 AM you wrote:
> >
> > Well instead of trying to help I better learn how to program
> > in Axiom - atleast.  I trying to implement a continued fraction
> > representation of the incomplete gamma function found in
> > Numerical Recipes for C:
> > http://www.library.cornell.edu/nr/bookcpdf/c6-4.pdf
> >
> > equation 6.2.7 but have had little success and thought you
> > might have some simple solution, here is my code;
> >
> > n:=10
> > num(a) == cons(1,[i*(i-a) for i in 1..])
> > den(a,x) == cons(x+1-a,[-(x-a+2*i+1) for i in 1..])
> > num5 := num(5)
> > den5 := den(5,10)
> > gamma := exp(-1.0)*(1.0)^5*continuedFraction(0,num5,den5)
> >
> > as you can see I don't even have a function to compute gamma
> > only a continued function that Axiom doesn't like.
> >
> > Thank you,
> >
> > Yigal Weinstein
> >
> >
>

```

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