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Distinction between associated Legendre and Ferrers functions #31637
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comment:7
I see three options here:
I advocate the latter option since it leads to less confusion for the end-user (and developer). Other than that, implementing connection formulas to Legendre (Ferrers) functions of second kind are also desirable. |
Dependencies: #25034 |
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As pointed out in #25034 and https://groups.google.com/g/sage-devel/c/IDtiGF6HB28/m/QWwnAeLJBAAJ there is currently a conflict of conventions.
The current implementation is in line with 1, but as mentioned above this source seems to be flawed and a distinction to Ferrers functions needs to be made (cf. 2 and 3).
More precisely, we want to implement solutions of the ODE 4. There are solutions on (-1,1) called "Ferrers functions" 2 and solutions on (1,oo) which can be extended to the complex plane without the slit
(-oo,1]
3. This distinction has not been made yet but yields to different formulas in different cases. The current formulas favor the Ferrers functions.Here are a few references to consider:
Depends on #25034
CC: @sagetrac-jcwomack @slel @egourgoulhon
Component: misc
Issue created by migration from https://trac.sagemath.org/ticket/31637
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