From 3205a96296a5e5f59dd34cb36f25a28e69d6a41f Mon Sep 17 00:00:00 2001 From: Shuhei Ohno Date: Wed, 29 May 2024 16:53:24 +0900 Subject: [PATCH] Fix docstring #49 --- src/PoschlTeller.jl | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/src/PoschlTeller.jl b/src/PoschlTeller.jl index b89c98c..5c3e66f 100644 --- a/src/PoschlTeller.jl +++ b/src/PoschlTeller.jl @@ -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) \ No newline at end of file +""" P(model::PoschlTeller, x; n=0, m=0) \ No newline at end of file