From 259169a2aee4c70d6b307308414a14101bd6e0e2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= <marek@necada.org>
Date: Mon, 8 Jul 2019 16:37:07 +0300
Subject: [PATCH] More entries to the table

Former-commit-id: 1c6af1e8c28a8146eb11e535183dcff7508e37b2
---
 notes/conventions.md         | 9 ++++++++-
 notes/mathjax_newcommands.js | 3 +++
 2 files changed, 11 insertions(+), 1 deletion(-)

diff --git a/notes/conventions.md b/notes/conventions.md
index 9efbf94..6588ad6 100644
--- a/notes/conventions.md
+++ b/notes/conventions.md
@@ -19,5 +19,12 @@ VSWF conventions
 	 P = \frac{1}{2k^2\eta_0\eta} \sum_n \left( \abs{\wckrout_n}^2 +\Re \left(\wckrout_n\wckrreg_n^{*}\right)\right)
  \f]	| The \f$ \wckrreg, \wckrout \f$ coefficients have dimension \f$ \mathrm{V/m} \f$. |
 | Reid \cite reid_electromagnetism_2016	|   |  	|   	|   	| 	| 	|
-| Taylor \cite taylor_optical_2011	|   | 	|   	|   	| 	| Different sign for regular/scattered waves! |
+| Taylor \cite taylor_optical_2011	| \f[
+	\wfet_{mn}^{(j)}	=	\frac{n(n+1)}{kr}\sqrt{\frac{2n+1}{4\pi}\frac{\left(n-m\right)!}{\left(n+m\right)!}}P_{n}^{m}\left(\cos\theta\right)e^{im\phi}z_{n}^{j}\left(kr\right)\uvec{r} \\
+		+\left[\tilde{\tau}_{mn}\left(\cos\theta\right)\uvec{\theta}+i\tilde{\pi}_{mn}\left(\cos\theta\right)\uvec{\phi}\right]e^{im\phi}\frac{1}{kr}\frac{\ud\left(kr\,z_{n}^{j}\left(kr\right)\right)}{\ud(kr)}, \\ 
+	\wfmt_{mn}^{(j)}	=	\left[i\tilde{\pi}_{mn}\left(\cos\theta\right)\uvec{\theta}-\tilde{\tau}_{mn}\left(\cos\theta\right)\uvec{\phi}\right]e^{im\phi}z_{n}^{j}\left(kr\right)
+\f]  | 	|   	| \f[ 
+	\vect E = \sum_{mn} \pr{-i \pr{\wcetreg_{mn}\wfetreg_{mn} + \wcmtreg_{mn}\wfmtreg{mn}} +i \pr{\wcetout_{mn}\wfetout_{mn} + \wcmtout_{mn}\wfmtout_{mn}}}, \\
+	\vect H = n_{ext}\sum_{mn} \pr{- \pr{\wcmtreg_{mn}\wfetreg_{mn} + \wcetreg_{mn}\wfmtreg{mn}} + \pr{\wcmtout_{mn}\wfetout_{mn} + \wcetout_{mn}\wfmtout_{mn}}},
+\f]  	| 	| Different sign for regular/scattered waves! Also WTF are the units of \f$ n_{ext} \f$? |
 
diff --git a/notes/mathjax_newcommands.js b/notes/mathjax_newcommands.js
index 7ed0961..3ce431b 100644
--- a/notes/mathjax_newcommands.js
+++ b/notes/mathjax_newcommands.js
@@ -5,6 +5,7 @@ MathJax.Hub.Config({
             abs: ["{\\left|{#1}\\right|}",1],
             ud: "{\\mathrm{d}}",
 	    pr: ["{\\left({#1}\\right)}", 1], // parentheses to save typing
+	    uvec: ["{\\mathbf{\\hat{#1}}}", 1],
             // Kristensson's VSWFs, complex version (2014 notes)
             wfkcreg: "{\\vect{v}}", // regular wave
             wfkcout: "{\\vect{u}}", // outgoing wave
@@ -18,6 +19,8 @@ MathJax.Hub.Config({
             wckrout: "{f}", // outgoing wave coeff
 
 	    // Taylor's VSWFs
+	    wfmt: "{\\widetilde{\\vect{M}}}",
+	    wfet: "{\\widetilde{\\vect{N}}}",
 	    wfmtreg: "{\\widetilde{\\vect{M}}^{(1)}}", // regular magnetic wave
 	    wfetreg: "{\\widetilde{\\vect{N}}^{(1)}}", // regular electric wave
 	    wfmtout: "{\\widetilde{\\vect{M}}^{(3)}}", // outgoing magnetic wave