jacobi_p expansion?



I can't think of any reasons why specfun should 
not be replaced by orthopoly. The main advantage 
of orthopoly over specfun is floating point evaluation.

(%i1) load("specfun")$
(%i2) jacobi_p(57,1/2,1/3,0.52);
(%o2)                          293237.1580243657
(%i3) float(jacobi_p(57,1/2,1/3,52/100));
(%o3)                          0.06384839164446
(%i4) 

(%i2) load("l:/orthopoly-0.94/orthopoly.lisp")$
(%i3) jacobi_p(57,1/2,1/3,0.52);
(%o3)          interval(0.06384839164446, 2.159480417194154E-14)
(%i4) orthopoly_returns_intervals : false$
(%i5) jacobi_p(57,1/2,1/3,0.52);
(%o5)                          0.06384839164446

The testing code for specfun is a subset of the testing code for 
orthopoly. And orthopoly has better user documentation.

Orthopoly doesn't do anything like 

    gen_laguerre(n,0,x) = laguerre(n,x)

Someday maybe ... But in view of RJF's comments about
automatic expansion, I should think a few things through
before I do anything like this.


Barton




Raymond Toy <raymond.toy@ericsson.com>
Sent by: maxima-admin@math.utexas.edu
12/03/2004 01:42 PM

 
        To:     Barton Willis <willisb@unk.edu>
        cc:     Maxima List <maxima@math.utexas.edu>
        Subject:        Re: [Maxima] jacobi_p expansion?


>>>>> "Barton" == Barton Willis <willisb@unk.edu> writes:

    Barton> (1) orthopoly isn't in the maxima distribution; get it from

Is there a reason why maxima shouldn't have orthopoly instead of
specfun?  I haven't tried it yet, but I would think it's not worse
than specfun.

A couple of things I wish specfun could do.  Perhaps orthopoly can do
this?

o gen_laguerre(n,0,x) = laguerre(n,x)
o gen_laguerre(n,1/2,x) = c*hermite(2*n,sqrt(x))
o various other relationships

Not sure if automatically doing this is a good idea or not, though.

    Barton> (3) If I weren't so slothful, I'd change orthopoly to make the 
functions 
    Barton> work by simplification ---- then the ev in %i3 wouldn't be 
needed.

I'm not sure, but I think it's beneficial that jacobi_p isn't
simplified.  While hyp.lisp isn't always smart enough to return
jacobi_p with suitable symbolic args, other parts of hyp.lisp or
hypgeo.lisp might be confused if a hypergeometric function that should
have simplified to jacobi_p was expanded out to polynomial instead of
a jacobi_p function.

But I also haven't looked at hypgeo.lisp much either, so I could be
totally wrong.

Ray


_______________________________________________
Maxima mailing list
Maxima@www.math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima