improved orthogonal functions

[sagetrac-fwclarke]

The defects in the code for the hermite function in
sage/functions/orthogonal_polys.py which were noted and corrected in
#2336 apply equally to the other functions in that file.

The attached patch applies the same fix that worked for hermite to the
following functions:

chebyshev_T,
chebyshev_U,
gen_laguerre,
gen_legendre_P,
gen_legendre_Q,
jacobi_P,
laguerre,
legendre_P,
legendre_Q,
ultraspherical

This allows these polynomials to take much more general
arguments; see the examples given for legendre_P.

The functions:

gen_legendre_P,
gen_legendre_Q,
legendre_Q

no longer yield a string representing a Maxima expression when the
argument is a variable.

For m > n the function gen_legendre_Q(n, m, x)
has to be computed independently of Maxima. This part of the code may
need improving.

The introductory documentation has not been changed.

Component: calculus

Keywords: orthogonal polynomials Maxima

Issue created by migration from https://trac.sagemath.org/ticket/3148

[sagetrac-fwclarke]

Attachment: sage-3148.patch.gz

[mwhansen]

comment:2

Looks good to me. All the tests pass, and the patch definitely simplifies the code.

[sagetrac-mabshoff]

comment:3

Merged in Sage 3.0.2.rc0