### update doc accourding to Tex MacDown settings

parent 7871eeca
 ... ... @@ -12,78 +12,75 @@ The original work by **Boris Leistedt** and **Jason D. McEwen** ([see the ArXiv Mathematics in summary ---------------- Any function \f\$f(r,\Omega)\f\$ square-integrable on \f\$\mathrm{B}^3 = \mathrm{R}^+ \times [0,\pi] \times [0,2\pi)\f\$ can be decomposed as: Any function \$f(r,\Omega)\$ square-integrable on \$\mathrm{B}^3 = \mathrm{R}^+ \times [0,\pi] \times [0,2\pi)\$ can be decomposed as: \f{eqnarray} \$\$\begin{eqnarray} f(r,\Omega) &=& \sum_{n=0}^\infty \sum_{l=0}^{\infty}\sum_{m=-l}^{l}\ f_{lmn}\ K_{lmn}(r,\Omega) \label{eq:FLagfulla}\\ f_{lmn} &=& \int_{\mathrm{B}^3} dr d\Omega\ r^2\ f(r,\Omega)\ K^\ast_{lmn}(r,\Omega) \label{eq:FLagfullb} \f} \end{eqnarray}\$\$ based on the orthogonality of the set of functions \f{equation} \$\$\begin{equation} K_{lmn}(r,\Omega) \equiv Y_{l,m}(\Omega)\times {\cal L}_n(r) \label{eq:FLagOrthoFunc} \f} using the spherical harmonic functions \f\$Y_{l,m}\f\$ and the genralized Laguerre functions \f\${\cal L}_n\f\$ \end{equation}\$\$ using the spherical harmonic functions \$Y_{l,m}\$ and the genralized Laguerre functions \${\cal L}_n\$ \f{eqnarray} \$\$\begin{eqnarray} Y_{l,m}(\Omega) &=& \lambda_{lm}(\theta) e^{i m\phi} = \sqrt{\frac{2 l +1}{4 \pi}\frac{(l-m)!}{(l+m)!}}P_l^m({\cos \theta}) e^{i m\phi} \\ {\cal L}_n(r) &=& \sqrt{\frac{n!}{(n+\alpha)!}} e^{-r/2} L_n^{(\alpha)}(r) \f} \end{eqnarray}\$\$ with \f\$ L_n^{(\alpha)}(r)\f\$ the generalized Laguerre polynomials (notice that by default \f\$ \alpha = 2\f\$). with \$ L_n^{(\alpha)}(r)\$ the generalized Laguerre polynomials (notice that by default \$ \alpha = 2\$). For bnad-limited functions the discret sums are truncated with \f\$ l
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