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 - 1, x))/(x**2 - 1)
In [7]: dlm = diff(legendre(m,x),x)
In [8]: dlm
Out[8]: m*(x*legendre(m, x) - legendre(m - 1, x))/(x**2 - 1)
In [9]: integrate(dlm*dln, (x, -1,1))
Probably we used one of your integration branches?
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