orthopoly documentation (was: Howto simplify Integral with jacobi polynomials)

On Saturday 12 July 2008, David Joyner wrote:
> I looked this up once and here is what I claim to be true:
>
>
> Jacobi polynomials are a class of orthogonal polynomials
> obtained from hypergeometric series in cases where the series
> is in fact finite:
> \[
> P_n^{(\alpha,\beta)}(z)
> =\frac{(\alpha+1)_n}{n!}
> \,_2F_1\left(-n,1+\alpha+\beta+n;\alpha+1;\frac{1-z}{2}\right) ,
> \]
> where $()_n$ is Pochhammer's symbol (for the rising factorial),
> (Abramowitz and Stegun p561.) and thus have the explicit expression
>
> \[
> P_n^{(\alpha,\beta)} (z)
> = \frac{\Gamma (\alpha+n+1)}{n!\Gamma (\alpha+\beta+n+1)}
> \sum_{m=0}^n {n\choose m}
> \frac{\Gamma (\alpha + \beta + n + m + 1)}{\Gamma (\alpha + m + 1)}
> \left(\frac{z-1}{2}\right)^m .
> \]
>
>
> If this is in any way wrong, I would really like to know.

I know what Jacobi polynomials are.

The point is orthogonal polynomials are only unique up to a factor.
If your problem depends on that factor,
you have to search the lisp source?????
find a copy of A&S????
Did you see the errata to Gradshteyn & Ryzhik 6th ed.?

I believe such things should be documented.

there is a function
orthopoly_weight

e.g. I found no possiblity to get the
highest coefficient of jacobi polynomials
	ratcoef(jacobi_p(n,a,b,x),x,n)
for an unknown integer n >= 0, 

why not have something similar 
for the functionality i listed in an earlier post?

I'm not criticizing the original authors of orthopoly,
I simply gave some opportunities for improving the orthopoly package.

Andre

>
> On Sat, Jul 12, 2008 at 7:45 AM, andre maute <andre.maute at gmx.de> wrote:
> > On Friday 11 July 2008, Michel Talon wrote:
> >> Raymond Toy (RT/EUS) wrote:
> >> > andre maute wrote:
> >> >> For the documentation, especially the orthopoly section,
> >> >> Abramowitz & Stegun (A&S) is freely available
> >> >> but Gradshteyn & Ryzhik and Merzbacher are not.
> >> >>
> >> >> Couldn't the documentation be a litlle bit more specific
> >> >> at least for the nonfree citations?
> >> >> Perhaps implementing the tables of A&S would help here also.
> >> >
> >> > I don't follow you.  What exactly are you suggesting here?  I, for
> >> > one, would like it if the documentation gave some definition for each
> >> > of the orthogonal polynomials.  The reference is nice, but, sometimes,
> >> > I have neither net access nor book access.
> >> >
> >> > Ray
> >>
> >> For the spherical harmonics, there is a very reasonable account in
> >> Wikipedia:
> >> http://en.wikipedia.org/wiki/Spherical_harmonics
> >> http://en.wikipedia.org/wiki/Associated_Legendre_functions
> >
> > I'm splitting the thread now.
> >
> > As stated in the wikipedia articles,
> > there are different normalizations in use,
> > Now could you tell me what kind of maxima uses,
> > it is not stated in the documentation
> >
> > Andre
> > _______________________________________________
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