The Jacobi polynomials jacobi_p(n,a,b,x) are defined for all real a & b,
but their weight function (1-x)^a (1+x)^b isn't integrable for a,b in
(-inf, -1].
Maybe for this reason, for a, b in (-inf,-1], specfun doesn't expand
jacobi_p(n,a,b,x) into a polynomial. But orthopoly will
(%i1) load("l:/orthopoly-0.94/orthopoly.lisp");
(%i2) hgfred([-2,2+1/2],[3/2],x);
(%o2) 8*jacobi_p(2,1/2,-1,1-2*x)/15
(%i3) ev(%);
(%o3) 7*x^2/3-10*x/3+1
Notes:
(1) orthopoly isn't in the maxima distribution; get it from
http://www.unk.edu/acad/math/people/willisb/
(2) In the past few days, Ray fixed some things in hyp.lisp.
You'll need a very new CVS maxima to get the result in %o2 .
(3) If I weren't so slothful, I'd change orthopoly to make the functions
work by simplification ---- then the ev in %i3 wouldn't be needed.
Barton
Raymond Toy <raymond.toy@ericsson.com>
Sent by: maxima-admin@math.utexas.edu
12/02/2004 04:04 PM
To: Maxima List <maxima@math.utexas.edu>
cc:
Subject: [Maxima] jacobi_p expansion?
jacobi_p(2,1/2,-1,1-2*x) is a polynomial (of course). But maxima
doesn't expand that out. Should it?
Note that if n is an integer, jacobi_p(n,1/2,-1,1-2*x) gives a series
expression, which I can then use via ev(%,n=2) to get a polynomial.
Ray
_______________________________________________
Maxima mailing list
Maxima@www.math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima