symbolic Laguerre / associated Laguerre polynomials

[rwst]

Not only is laguerre(n,x) not symbolic, a naive implementation is already 2x as fast at n=100 and 10x at n=1000:

R.<x> = PolynomialRing(QQ, 'x')
def lag(n):
    return R([binomial(n,k)*(-1)^k/factorial(k) for k in xrange(n+1)])

• https://en.wikipedia.org/wiki/Laguerre_polynomials
• http://mathworld.wolfram.com/LaguerrePolynomial.html
• http://mathworld.wolfram.com/AssociatedLaguerrePolynomial.html

Depends on #17953

Component: symbolics

Keywords: special, function, holonomic, orthogonal

Author: Ralf Stephan

Branch/Commit: f0d809f

Reviewer: Marc Mezzarobba

Issue created by migration from https://trac.sagemath.org/ticket/17151

[rwst]

Description changed:

--- 
+++ 
@@ -6,3 +6,6 @@
     return R([binomial(n,k)*(-1)^k/factorial(k) for k in xrange(n+1)])
 ```
 
+* https://en.wikipedia.org/wiki/Laguerre_polynomials
+* http://mathworld.wolfram.com/LaguerrePolynomial.html
+* http://mathworld.wolfram.com/AssociatedLaguerrePolynomial.html

[rwst]

Branch: u/rws/symbolic_laguerre___associated_laguerre_polynomials

[rwst]

New commits:

6d10729	Simplify numerical evaluation of BuiltinFunctions
b6e1ed4	Merge remote-tracking branches 'origin/u/jdemeyer/ticket/17131' and 'origin/u/jdemeyer/ticket/17133' into ticket/17130
04b2b37	Merge branch 'u/jdemeyer/ticket/17130' of trac.sagemath.org:sage into t/17151/symbolic_laguerre___associated_laguerre_polynomials
3d3d1fa	17151: skeleton impl.
b3edc51	17151: implement symbolic Laguerre pol.
c8beac2	17151: implement laguerre(n,x)
1626a8b	17151: implement gen_laguerre

[rwst]

Commit: 1626a8b

[rwst]

Author: Ralf Stephan

[sagetrac-git]

Changed commit from 1626a8b to f727de5

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

f727de5

17151: reduce evalf logic further; fix merge conflict

[kcrisman]

comment:6

For some reason this branch is red.