jishnub/legendrepolynomials.jl

Legendre polynomials and associated Legendre polynomials computed using 3-term recursions

legendrepolynomials.jl's Issues

Legendre Polynomials are defined for arguments lying in -1 ⩽ x ⩽ 1

I got this error:

julia> Pl(1.2,3)
DomainError with 1.2:
Legendre Polynomials are defined for arguments lying in -1 ⩽ x ⩽ 1

I am somewhat perplexed. A polynomial defined on -1 ⩽ x ⩽ 1 is of course defined for all complex x, and in particular for x=1.2. Evaluating a Legendre polynomial at x=1.2 is particularly straightforward when using recurrence relations. I checked the source code of this library and it looks to me like it uses the recurrence relation. I'm not sure why it refuses to work at x=1.2.

Is this a bug?

TagBot trigger issue

This issue is used to trigger TagBot; feel free to unsubscribe.

If you haven't already, you should update your TagBot.yml to include issue comment triggers.
Please see this post on Discourse for instructions and more details.

If you'd like for me to do this for you, comment TagBot fix on this issue.
I'll open a PR within a few hours, please be patient!

Specify norm used in the Legendre polynomials

Coming from Matlab I was uncertain which norm is used in this package, since Matlab allows 3 norms:

1. No normalization
2. Schmidt seminormalized
3. Fully normalized

I figured out the normalization used in Julia by calling Plm and comparing the result to Matlab (no normalization is used), but it may be useful to have it specified in print.

slow compared to AssociatedLegendrePolynomials.jl and to GSL.jl

As described in this discourse post, this package currently seems to be 4–5 times slower than AssociatedLegendrePolynomials.jl or GSL.jl.

Adding derivatives of associated Legendre functions

It would be helpful to have functions like dnPlm and the collect- methods for arbitrary n-th derivatives of the associated Legendre functions.