On 13/04/13 14:36, someone wrote: >> I recently had a need for Jacobi polynomials with the property that >> >> int(P(i, a, b, x)*P(j, a, b, x)*(1-x)^a*(1+b)^b, (x, -1, 1) = >> delta_ij >> >> with the key element being the normalization factor. Would it be >> possible to get this upstream (it is a pain to code up!), for example >> as a norm=True kwarg? > > I think that this should go upstream and I'm preparing a PR for this. > But there are a few open points: > > - What about the *symbolic* representation? (Unevaluated P(j,a,b,x) with j,a,b > unspecified.) Are they normalized or not? Does the flag take action here > too? > How to get from one to the other form? (Something like "rewrite") > And how to differ them in pretty prints, latex etc?
A convention I often use is \hat{P} for when the polynomial is
normalized in the sense of orthonormality.
> - What if we have more different normalizations?
> F.e. for Hermite polynomials we have the probabilists' and
> the physicists' Hermite polynomials. [1]
> For spherical harmonics there are even more conventions [2].
> How should we call the flag? And what values should it take?
> Maybe "normalization" with enumerated values "none", "geodesic", "magnetic"
> etc.
> But these values could be different for each polynomial type!
This is a good question -- and one which I do not have a good solution
to. A norm='flag' looks like a good solution so long as we can come up
with a good set of naming conventions.
Regards, Freddie.
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