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Fix docstring #49
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ohno committed May 29, 2024
1 parent 2eaf6f4 commit 3205a96
Showing 1 changed file with 9 additions and 9 deletions.
18 changes: 9 additions & 9 deletions src/PoschlTeller.jl
Original file line number Diff line number Diff line change
Expand Up @@ -111,13 +111,13 @@ where ``\mu = \mu(n) = n_\mathrm{max}-n+1``, and ``n_\mathrm{max} = \left\lfloor
Associated Legendre polynomials are the associated Legendre functions for integer indices. Here we use the same notation of the associated Legendre functions as in the model HydrogenAtom.
```math
\begin{aligned}
P_n^m(x)
&= \left( 1-x^2 \right)^{m/2} \frac{\mathrm{d}^m}{\mathrm{d}x^m} P_n(x) \\
&= \left( 1-x^2 \right)^{m/2} \frac{\mathrm{d}^m}{\mathrm{d}x^m} \frac{1}{2^n n!} \frac{\mathrm{d}^n}{\mathrm{d}x ^n} \left[ \left( x^2-1 \right)^n \right] \\
&= \frac{1}{2^n} (1-x^2)^{m/2} \sum_{j=0}^{\left\lfloor\frac{n-m}{2}\right\rfloor} (-1)^j \frac{(2n-2j)!}{j! (n-j)! (n-2j-m)!} x^{(n-2j-m)}.
\end{aligned}
```
```math
\begin{aligned}
P_n^m(x)
&= \left( 1-x^2 \right)^{m/2} \frac{\mathrm{d}^m}{\mathrm{d}x^m} P_n(x) \\
&= \left( 1-x^2 \right)^{m/2} \frac{\mathrm{d}^m}{\mathrm{d}x^m} \frac{1}{2^n n!} \frac{\mathrm{d}^n}{\mathrm{d}x ^n} \left[ \left( x^2-1 \right)^n \right] \\
&= \frac{1}{2^n} (1-x^2)^{m/2} \sum_{j=0}^{\left\lfloor\frac{n-m}{2}\right\rfloor} (-1)^j \frac{(2n-2j)!}{j! (n-j)! (n-2j-m)!} x^{(n-2j-m)}.
\end{aligned}
```
""" P(model::PoschlTeller, x; n=0, m=0)
""" P(model::PoschlTeller, x; n=0, m=0)

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