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+%%
+%%  Examples of a widetext environment for setting wide equations in the asmeconf class.
+%%  Copyright (c) 2021 John H. Lienhard.  Use under the MIT license: https://ctan.org/license/mit 
+%%
+%%  USAGE: 	* \begin{widetext} ...wide material here... \end{widetext}
+%%	OPTIONAL ARGUMENTS: 
+%%			* \begin{widetext[N] .. changes upper/lower separation of wide material from default 5pt to Npt
+%%			* \begin{widetext}[][tbn]: t = top line only; b = bottom line only; n = no lines.  BOTH arguments are REQUIRED, even if first is left empty.
+%%
+%%	The widetext environment can only appear once per page. It clashes with floats and footnotes, as discussed herein.
+%%
+%%  NB: the strip environment from cuted is incompatible with the [lineno] option to asmeconf!
+
+\documentclass[nofoot,colorlinks,balance,pdf-a]{asmeconf}
+
+\def\ACwidetextversion{1.0}
+\def\ACwidetextdate{January 10, 2022}
+
+\usepackage{lipsum}% Latin filler text
+\usepackage{asmewide}
+
+
+\begin{filecontents}{asme-wide-equations.bib}
+@online{lienhard2021,
+  author = {Lienhard, John H., V},
+  title = {{\texttt{asmeconf}}: A template for {ASME} conference papers},
+  organization = {Comprehensive \TeX\ Archive Network},
+  version = {{\versionno}},
+  year = {2021},
+  url = {https://ctan.org/pkg/asmeconf},
+  urldate = {{\today}},
+}      
+@online{tolucsis1,
+  author = {Sigitas Tolu\v{s}is},
+  year = {2021},
+  title = {The \texttt{cuted} package},
+  version = {2.0},
+  organization = {Comprehensive \TeX\ Archive Network},
+  url = {https://ctan.org/pkg/cuted},
+  urldate = {Dec. 30, 2021},
+}
+@online{tolucsis2,
+  author = {Sigitas Tolu\v{s}is},
+  year = {2021},
+  title = {The \texttt{sttools} collection},
+  version = {3.0},
+  organization = {Comprehensive \TeX\ Archive Network},
+  url = {https://ctan.org/pkg/sttools},
+  urldate = {Dec. 30, 2021},
+}
+@book{stakgold,
+author = {Ivar Stakgold},
+title = {Boundary Value Problems of Mathematical Physics},
+year = {1967},
+publisher = {Macmillan},
+address = {New York},
+}
+\end{filecontents}
+
+\hypersetup{%
+	pdfauthor={John H. Lienhard},                       		     
+	pdftitle={Wide Equations in asmeconf.cls},                 
+	pdfkeywords={ASME conference paper, LaTeX template, wide equations, widetext},
+	pdfsubject = {Examples of setting wide equations in the asmeconf LaTeX template},
+	pdfurl={https://ctan.org/pkg/asmeconf},
+	pdflicenseurl={https://ctan.org/pkg/asmeconf},
+}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{document}
+
+\ConfName{Proceedings of the \texttt{asmeconf}\linebreak International Examples Congress and Exposition}
+\ConfAcronym{AIECE22}
+\ConfDate{January 10, 2022}
+\ConfCity{Cambridge, MA}
+\PaperNo{AIECE2022-0003}
+
+\SetAuthors{John H.\ Lienhard V\affil{}\CorrespondingAuthor{lienhard@mit.edu}}
+\SetAffiliation{}{Fellow of ASME \\
+Rohsenow Kendall Heat Transfer Laboratory, \\
+Department of Mechanical Engineering,\\
+Massachusetts Institute of Technology, \\
+Cambridge, MA 02139 USA 
+}
+
+\title{Wide Equations in asmeconf.cls}
+\maketitle
+
+\versionfootnote{Examples of \texttt{widetext} in \texttt{asmeconf}. Version \ACwidetextversion, \ACwidetextdate}
+
+\keywords{ASME conference paper, \LaTeX\ template, wide equations, asmeconf}
+    
+\begin{abstract}
+This paper gives several examples of typesetting very wide equations with {\upshape\LaTeX} in the {\upshape\texttt{asmeconf}} class~{\upshape\cite{lienhard2021}} using {\upshape\texttt{asmewide.sty}}.
+The style defines a the {\upshape\texttt{widetext}} environment, built on the 2021 release of {\upshape\texttt{cuted.sty}~\cite{tolucsis1}} from the
+{\upshape\texttt{sttools}} bundle~{\upshape\cite{tolucsis2}}, which is available from CTAN, \hrefurl{http://ctan.org}{ctan.org}.  
+Significant hand-fitting around pagebreaks, floats, and footnotes is required to obtain good results. Users can change the source file to explore the behavior and limitations of the {\upshape\texttt{widetext}} environment. \textcolor{red}{Only the text in \textbf{red} in this document meant 
+to be read---the rest is simply filler to aid in layout.}
+\end{abstract}
+
+
+\section{Introduction}
+\lipsum[1-2]
+\section{Section}
+\lipsum[3]
+
+%%%%%%%%%%%%%%%%%  begin two column figure  %%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{figure*}[t]
+\begin{subfigure}[c]{0.495\textwidth}
+\centering{\includegraphics{zonal-harmonic2.pdf}}%
+\subcaption{\label{fig:zonal}}
+\end{subfigure}
+%%%%%%%% don't leave a break here
+\begin{subfigure}[c]{0.495\textwidth}
+\centering{\includegraphics{tesseral-harmonic.pdf}}%
+\subcaption{\label{fig:tesseral}}%
+\end{subfigure}%
+\caption{A figure with two subfigures: (a) Zonal harmonic $n=1, m=0$, (b) Tesseral harmonic $n=2, m=3$. See Appendix~\ref{sec:sph-har}.\label{fig:1}}
+\end{figure*}
+%%%%%%%%%%%%%%%%%%%  end two column figure  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\lipsum[4]
+\subsection{Subsection}
+\lipsum[5-6]
+
+
+%%%%%%%%%%%%%%%%%%%%  Example WT1  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Single Wide Equation on the Page}
+
+\textcolor{red}{Equation~\eqref{eqn:WT1} is an equation with a matrix that is too large to fit into one column. A multiline math environment will not help because the equation cannot be broken into parts that each fit into a column. The \texttt{widetext} environment solves the problem.}  
+
+\textcolor{red}{A two-column wide figure, Fig.~\ref{fig:1}, has floated from a previous page to the top of this page, but does not interfere with the \texttt{widetext} material (a one column float would interfere).}
+
+\begin{widetext}
+\begin{equation}\label{eqn:WT1}
+\mathbf{WT1:}\quad
+\mathfrak{W}(\bm{\Phi})= \begin{Vmatrix}
+\dfrac\varphi{(\varphi_1,\varepsilon_1)}			& 0 												& \hdotsfor{4} 	& 0 			&	\\[\jot]
+\dfrac{\varphi k_{21}}{(\varphi_2,\varepsilon_1)}	& \dfrac\varphi{(\varphi_2,\varepsilon_2)}			& 0 			& \hdotsfor{3} 	& 0 \\[\jot]
+\dfrac{\varphi k_{31}}{(\varphi_3,\varepsilon_1)}	&\dfrac{\varphi k_{32}}{(\varphi_3,\varepsilon_2)}	& \dfrac\varphi{(\varphi_3,\varepsilon_3)}& 0 & \hdotsfor{2} & 0 \\[\jot]
+\vdots 	&  &  & \smash{\rotatebox{15}{$\ddots$}} &  & & \vdots \\[\jot]
+\dfrac{\varphi k_{n-2\, 1}}{(\varphi_{n-2},\varepsilon_1)}	&
+\dfrac{\varphi k_{n-2\, 2}}{(\varphi_{n-2},\varepsilon_2)}	&\hdotsfor{1} & \dfrac{\varphi k_{n-2\,n-3}}{(\varphi_{n-2},\varepsilon_{n-3})} & \dfrac\varphi{(\varphi_{n-2},\varepsilon_{n-2})}& 0& 0 \\[\jot]
+\dfrac{\varphi k_{n-1\, 1}}{(\varphi_{n-1},\varepsilon_1)}	& \dfrac{\varphi k_{n-1\, 2}}{(\varphi_{n-1},\varepsilon_2)} &\hdotsfor{2} & 
+\dfrac{\varphi k_{n-1\,n-2}}{(\varphi_{n-1},\varepsilon_{n-2})}& \dfrac{\varphi}{(\varphi_{n-1},\varepsilon_{n-1})} & 0 \\[\jot]
+\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}	& \dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}	& \hdotsfor{3}	&
+\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})} & \dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
+\end{Vmatrix}
+\end{equation}
+\end{widetext}
+
+\lipsum[7-8]
+
+
+%%%%%%%%%%%%%%%%%%%%  Examples WT2 & WT3  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Two Wide Equations on the Page}
+
+\lipsum[9-10]
+
+\begin{widetext} 
+\begin{equation}\mathbf{WT2:}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy
+ \ne \frac{1}{\sqrt{\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+  \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}}
+\end{equation}
+
+\textcolor{red}{In this case, we have a pair of wide equations on the same page.  The \texttt{widetext} environment cannot be used twice on the same page! To resolve the conflict, we remain in single column mode between the two equations.}
+
+\textcolor{red}{This page also includes a single column float, Table~\ref{tab:2}. This float must come after the \texttt{widetext} environment. We use the \texttt{\textbackslash begin\{table\}[b]} option to force the table to the bottom of the column. The two column table, Table~\ref{tab:4}, floats to the top of the next page and creates no problems.}
+
+\begin{equation}\mathbf{WT3:}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy
+ \ne \frac{1}{\sqrt{\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+  \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}}
+\end{equation}
+\end{widetext}
+
+
+%%%%%%%%%%%%%%% begin single column table %%%%%%%%%%%%%%%%%%%%%%
+\begin{table}[b]
+\caption{Table with more complicated columns}\label{tab:2}%
+\centering{%
+\begin{tabular}{!{\hspace*{0.5cm}} >{\raggedright\hangindent=1em} p{3cm} d{3} @{\hspace*{1cm}} d{3} !{\hspace*{0.5cm}}}
+\hline\hline
+\rule{0pt}{10pt} Experiment & \multicolumn{1}{c@{\hspace*{1cm}}}{$u$ [m/s]} & \multicolumn{1}{c!{\hspace*{0.5cm}}}{$T$ [\textdegree C]} \\[1pt]
+\hline
+The first experiment we ran this morning   & 124.3     &   68.3   \rule{0pt}{10pt} \\
+The second experiment we ran this morning  &  82.50    &  103.46  \\
+Our competitor's data                      &  72.321   &  141.384 \\[1pt]
+\hline\hline
+\end{tabular}
+}
+\end{table}
+%%%%%%%%%%%%%%%% end table  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%% begin two column table %%%%%%%%%%%%%%%%%%%%%%%%% 
+\begin{table*}[t]
+\caption{A table spanning two columns}\label{tab:4}%
+\centering{%
+\begin{tabular*}{0.8\textwidth}{@{\hspace*{1.5em}}@{\extracolsep{\fill}}ccc!{\hspace*{3.em}}ccc@{\hspace*{1.5em}}}
+\hline\hline
+\multicolumn{1}{@{\hspace*{1.5em}}c}{$x$\rule{0pt}{11pt}} &
+\multicolumn{1}{c}{$\textrm{erf}(x)$} &
+\multicolumn{1}{c!{\hspace*{3.em}}}{$\textrm{erfc}(x)$} &
+\multicolumn{1}{c}{$x$} &
+\multicolumn{1}{c}{$\textrm{erf}(x)$} &
+\multicolumn{1}{c@{\hspace*{1.5em}}}{$\textrm{erfc}(x)$} \\ \hline
+0.00 & 0.00000 & 1.00000 & 1.10 & 0.88021 & 0.11980\rule{0pt}{11pt} \\
+0.05 & 0.05637 & 0.94363 & 1.20 & 0.91031 & 0.08969 \\
+0.10 & 0.11246 & 0.88754 & 1.30 & 0.93401 & 0.06599 \\
+0.15 & 0.16800 & 0.83200 & 1.40 & 0.95229 & 0.04771 \\
+0.20 & 0.22270 & 0.77730 & 1.50 & 0.96611 & 0.03389 \\
+0.30 & 0.32863 & 0.67137 & 1.60 & 0.97635 & 0.02365 \\
+0.40 & 0.42839 & 0.57161 & 1.70 & 0.98379 & 0.01621 \\
+0.50 & 0.52050 & 0.47950 & 1.80 & 0.98909 & 0.01091 \\
+0.60 & 0.60386 & 0.39614 & 1.82\makebox[0pt][l]{14} & 0.99000 & 0.01000 \\
+0.70 & 0.67780 & 0.32220 & 1.90 & 0.99279 & 0.00721 \\
+0.80 & 0.74210 & 0.25790 & 2.00 & 0.99532 & 0.00468 \\
+0.90 & 0.79691 & 0.20309 & 2.50 & 0.99959 & 0.00041 \\
+1.00 & 0.84270 & 0.15730 & 3.00 & 0.99998 & 0.00002 \\[2pt]
+\hline\hline
+\end{tabular*}
+}
+\end{table*}
+%%%%%%%%%%%%%%%% end table %%%%%%%%%%%%%%%%%%% 
+
+\lipsum[17-24]
+
+
+%%%%%%%%%%%%%%%%%%%%  Examples WT4 & WT5  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Wide Equation Pair Split Across Page Break and Followed by Wide Equation}
+
+\textcolor{red}{Here, we turn off automatic top line so that it does not appear again at the top of the next page: \texttt{\textbackslash TopLineOff}. We instead issue a command to create the top line inside the \texttt{widetext} environment, \texttt{\textbackslash LineAbove}.  We must remember to restore the automatic top line after we exit the \texttt{widetext} environment: \texttt{\textbackslash TopLineOn}.}
+
+\textcolor{red}{The \texttt{\textbackslash newpage} command may optionally be used between the equations to force the second one onto the following page, e.g., try removing the source code line \texttt{\textbackslash lipsum[27]} with and without \texttt{\textbackslash newpage}.}
+
+\begin{widetext}
+\begin{equation}\mathbf{WT4:}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy
+ \ne \frac{1}{\sqrt{\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}}
+\end{equation}%\newpage
+\begin{equation}\mathbf{WT5:}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy
+ \ne \frac{1}{\sqrt{\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+  \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}}
+\end{equation}
+
+\textcolor{red}{In this case, we again have a pair of wide equations on the same page, so we stay in single column mode
+until both are done\footnotemark. The single column table, Table~\ref{tab:3}, is forced to the bottom of the page using the \texttt{[b]} option.}
+
+\lipsum[32-33]
+
+\begin{equation}\mathbf{WT6:}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy
+ \ne \frac{1}{\sqrt{\int_a^b\biggl\{g^2\int_a^bf^2+f^2
+  \int_a^b g^2-2fg\int_a^b fg\biggr\}\,dy}}
+\end{equation}
+\end{widetext}
+\footnotetext{\textcolor{red}{The code from \texttt{cuted.sty} doesn't play well with footnotes, so we issue a \texttt{\textbackslash footnotemark} command inside the wide material and a separate \texttt{\textbackslash footnotetext\{..\}} command outside the wide environment.}}%
+\lipsum[34-37]
+
+%%%%%%%%%%%%%%%%%%%  begin linewidth table  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{table}[b]
+\newcolumntype{C}{>{$}c<{$}} % math-mode version of "c" column type, from array package
+\caption{\label{tab:3}Table at full column width with columns in math mode}
+\centering{%
+\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}CCCC@{\extracolsep{\fill}}}
+\hline\hline
+X_{z} & X_{c} & X_{c,m} & X_{c,2}\rule{0pt}{11pt}\\
+ 3.92069  & 5.70943 & 6.32429 & 7.08757\\[2pt]
+\varepsilon (T_1)  & \varepsilon^i (T_1) & \varepsilon^i (T_m) & \alpha (T_1, T_2)\\
+0.7258 & 0.6237 & 0.6807 & 0.7964 \\[2pt]
+q_\textrm{gray}  & q_\textrm{int, $T_1$} & q_\textrm{int, $T_m$} & q_\textrm{exact}\\
+400.2 & 462.1 & 371.0 & 371.8 \\[1pt]
+\hline\hline
+\end{tabular*}
+}
+\end{table}
+%%%%%%%%%%%%%%%%%%%%  end linewidth table %%%%%%%%%%%%%%%%%%%%%%%
+
+\lipsum[40-48]
+
+\textcolor{red}{For eqn.~\eqref{eqn:WT7}, we drop the bottom line, keeping the top line and increasing the vertical space a bit: \texttt{\textbackslash begin\{widetext\}[8][t]}.}
+
+\begin{widetext}[8][t]
+\begin{equation}\label{eqn:WT7}
+\mathbf{WT7:}\quad
+\cfrac{1}{1+ \cfrac{1}{abcxyz+(ax^2-by^3+cz^4)(\alpha\chi^2-\beta\upsilon^3+\kappa\zeta^4)(ax^4-by^3+cz^2)(a^2x^2-by^3+c^2z^2)}}
+\end{equation}
+\end{widetext}
+
+\lipsum[50-60]
+
+\textcolor{red}{In this case, we drop the top line: \texttt{\textbackslash begin\{widetext\}[][b]}.}
+
+\vskip 80pt% <== an extra skip to push this widetext over the edge
+
+\begin{widetext}[][b]
+\begin{equation}\label{eqn:WT8}
+\mathbf{WT8:}\quad
+\mathfrak{W}(\bm{\Phi})= \begin{Vmatrix}
+\dfrac\varphi{(\varphi_1,\varepsilon_1)}			& 0 												& \hdotsfor{4} 	& 0 			&	\\[\jot]
+\dfrac{\varphi k_{21}}{(\varphi_2,\varepsilon_1)}	& \dfrac\varphi{(\varphi_2,\varepsilon_2)}			& 0 			& \hdotsfor{3} 	& 0 \\[\jot]
+\dfrac{\varphi k_{31}}{(\varphi_3,\varepsilon_1)}	&\dfrac{\varphi k_{32}}{(\varphi_3,\varepsilon_2)}	& \dfrac\varphi{(\varphi_3,\varepsilon_3)}& 0 & \hdotsfor{2} & 0 \\[\jot]
+\vdots 	&  &  & \smash{\rotatebox{15}{$\ddots$}} &  & & \vdots \\[\jot]
+\dfrac{\varphi k_{n-2\, 1}}{(\varphi_{n-2},\varepsilon_1)}	&
+\dfrac{\varphi k_{n-2\, 2}}{(\varphi_{n-2},\varepsilon_2)}	&\hdotsfor{1} & \dfrac{\varphi k_{n-2\,n-3}}{(\varphi_{n-2},\varepsilon_{n-3})} & \dfrac\varphi{(\varphi_{n-2},\varepsilon_{n-2})}& 0& 0 \\[\jot]
+\dfrac{\varphi k_{n-1\, 1}}{(\varphi_{n-1},\varepsilon_1)}	& \dfrac{\varphi k_{n-1\, 2}}{(\varphi_{n-1},\varepsilon_2)} &\hdotsfor{2} & 
+\dfrac{\varphi k_{n-1\,n-2}}{(\varphi_{n-1},\varepsilon_{n-2})}& \dfrac{\varphi}{(\varphi_{n-1},\varepsilon_{n-1})} & 0 \\[\jot]
+\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}	& \dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}	& \hdotsfor{3}	&
+\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})} & \dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
+\end{Vmatrix}
+\end{equation}
+\end{widetext}
+
+\lipsum[55-56]
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\appendix  
+\section{Spherical harmonics\label{sec:sph-har}}
+
+Without getting into the details, a regular function $f(\theta,\phi)$ on the surface of the unit sphere may be written
+\begin{equation}
+f(\theta,\phi) = \sum_{n=0}^\infty \sum_{m=-n}^n f_{m,n} Y_n^m(\theta,\phi)
+\end{equation}
+for $Y_n^m(\theta,\phi) = e^{i m\phi}P^{|m|}_n(\cos\theta)$, for $|m|<n$. The case $n=3$, $m=2$ (a \textit{tesseral harmonic}) is shown in Fig.~\ref{fig:tesseral}.
+
+These functions are orthogonal, with the normalization constant~\cite[App.~A]{stakgold}:
+\begin{equation}
+N_{m,n}=\int_0^{2\pi}\!\!d\phi\int_0^{\pi}\!\!d\theta \sin\theta\, \big|Y^m_n(\theta,\phi)\big|^2 = \frac{4\pi (n+|m|)!}{(2n+1)(n-|m|)!}
+\end{equation} 
+
+If $f$ is independent of the azimuthal angle $\phi$, the solution appears in ordinary Legendre polynomials, $P_n$, rather than associated Legendre polynomials, $P^m_n$ ($P^0_n = P_n$):
+\begin{equation}
+f(\theta) = \sum_{n=0}^\infty f_n\, P_n(\cos\theta)
+\end{equation}
+The terms in this series are called \textit{zonal harmonics}.
+
+%%%%%%%%%%%%%%%%%%%%  bibliography  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\bibliographystyle{asmeconf}
+\bibliography{asme-wide-equations} 
+
+
+\end{document}