improved orthogonal functions

[5ef57b06-33a8-4a32-80d2-0f5ab07e80d9]

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

[5ef57b06-33a8-4a32-80d2-0f5ab07e80d9]

Attachment: sage-3148.patch.gz

[mwhansen]

comment:2

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

[85eec1a4-3d04-4b4d-b711-d4db03337c41]

comment:3

Merged in Sage 3.0.2.rc0