Opened 2 months ago
Last modified 2 months ago
#31637 new enhancement
Distinction between associated Legendre and Ferrers functions
Reported by: | gh-mjungmath | Owned by: | |
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Priority: | major | Milestone: | sage-9.4 |
Component: | misc | Keywords: | |
Cc: | jcwomack, slelievre, egourgoulhon | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | #25034 | Stopgaps: |
Description (last modified by )
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:
- [1]: https://mathworld.wolfram.com/AssociatedLegendrePolynomial.html (probably flawed?)
- [2]: https://dlmf.nist.gov/14.3#E1
- [3]: https://dlmf.nist.gov/14.21#i.p1
- [4]: https://dlmf.nist.gov/14.2#E2
- [5]: https://en.wikipedia.org/wiki/Associated_Legendre_polynomials
- [6]: http://www.math.ubc.ca/~cbm/aands/page_332.htm
Change History (9)
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comment:8 Changed 2 months ago by
- Milestone changed from sage-9.3 to sage-9.4
comment:9 Changed 2 months ago by
- Dependencies set to #25034
I see three options here:
ferrers_func
andgen_legendre_P
.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.