There is an old open PR:
http://github.com/sympy/sympy/pull/1026
which tries to make orthogonal polynomials work
for symbolic order 'n'. An open question is
when to apply simplifications like:
L_n(-x) --- (-1)**n * L_n(x)
L_{-n}(x) --- L_{n-1}(x)
Do we want to have this:
a) at
No, at the moment both options do not allow to
compute the orthogonality integrals :-/
@asmeurer: I remember we once tried
computing that:
In [2]: n = Symbol(n)
In [3]: m = Symbol(m)
In [4]: x = Symbol(x)
In [5]: dln = diff(legendre(n,x),x)
In [6]: dln
Out[6]: n*(x*legendre(n, x) - legendre(n -
What if either argument is something like x - y or y - x? Would those
both be canonicalized to the same thing (with either choice)?
No.
a) We pull out some factors and get legendre objects of same argument:
In [6]: legendre(n, y-x)
Out[6]: (-1)**n*legendre(n, x - y)
In [7]: legendre(n, x-y)
Which names should we choose for the elliptic integral functions in PR
1408?
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A first start:
http://github.com/sympy/sympy/pull/1408
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The problem I see is *how* to add these to the integration routines.
There is no nice Meijer-G representation. And I suppose that Risch
can not handle these. At least not w/o major extensions.
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