Skip to content

Unify list in index.md #29

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 1 commit into from
Feb 11, 2025
Merged
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
12 changes: 6 additions & 6 deletions docs/src/index.md
Original file line number Diff line number Diff line change
Expand Up @@ -159,17 +159,17 @@ The normalization options accepted are

* `norm = Val(:standard)`: standard, unnormalized polynomials. This is the default option. Choosing this option will lead to the standard Legendre or associated Legendre polynomials that satisfy ``P_\ell(0)=1`` and ``P_{\ell0}(0)=1``
* `norm = Val(:normalized)`: fully normalized polynomials, with an L2 norm of 1. These are defined as
```math
```math
\bar{P}_{\ell m}\left(x\right)=\sqrt{\frac{2\ell+1}{2}\frac{\left(\ell-m\right)!}{\left(\ell+m\right)!}}P_{\ell m}\left(x\right)
```
```
* `norm = Val(:schmidtquasi)`: Schmidt quasi-normalized polynomials, also known as Schmidt semi-normalized polynomials. These have an L2 norm of ``\sqrt{2(2-\delta_{m0})/(2\ell+1)}``. These are defined as
```math
```math
\bar{P}_{\ell m}\left(x\right)=\sqrt{\left(2-\delta_{m0}\right)\frac{\left(\ell-m\right)!}{\left(\ell+m\right)!}}P_{\ell m}\left(x\right)
```
```
* `norm = Val(:schmidt)`: Schmidt normalized polynomials. These have an L2 norm of ``\sqrt{2(2-\delta_{m0})}``. These are defined as
```math
```math
\bar{P}_{\ell m}\left(x\right)=\sqrt{\left(2-\delta_{m0}\right)\left(2\ell+1\right)\frac{\left(\ell-m\right)!}{\left(\ell+m\right)!}}P_{\ell m}\left(x\right)
```
```

!!! note
Irrespective of the norm specified, the 3-term recursion relations used are stable ones,
Expand Down
Loading