![Make4HT - 带有 LaTeX 方程式和 MathML 输出的 HTML](https://linux22.com/image/467524/Make4HT%20-%20%E5%B8%A6%E6%9C%89%20LaTeX%20%E6%96%B9%E7%A8%8B%E5%BC%8F%E5%92%8C%20MathML%20%E8%BE%93%E5%87%BA%E7%9A%84%20HTML.png)
我正在尝试根据以下给出的出色解决方案将 HTML 输出转换为 MathML 和 TeX 方程式米哈尔.h21在下面的帖子中
我在转换 HTML 时遇到问题
- 使用时
\begin{equation}/begin{equation*}
显示错误
! Missing } inserted.
}
l.26 \end
{equation*}
对于 Double
$$
使用的方程,TeX 方程部分未在 HTML 输出中转换需要重新配置
<eqno id="x1-3r2">(1)</eqno>
所有显示编号方程/环境的方程编号(标签)(这是为了清理目的,将方程标签移到 MathML 之外并重组 XML 标签)<display-math><label>..<label><mathML>...</mathML><tex-math>...</tex-math>
这是我的 MWE:
我正在运行一个文件make4ht
-make4ht -l -a debug -c myconfig.cfg Sample.tex
\documentclass[9pt]{book}
\usepackage[utf8]{inputenc}
\usepackage{hyperref}
\usepackage{amsmath,amssymb}
\usepackage{xspace}
\newcommand\eqannotate[1]{#1}
\begin{document}
Display equation with doble dollar
$$
a+b=c
$$
Display equation (equation env)
\begin{equation}
x+y=1
\end{equation}
Display equation (equation env)
\begin{equation*}
x+y=z
\end{equation*}
eqnarray environment
\begin{eqnarray}
x+y=1
\end{eqnarray}
display equation
\[
d+f=g
\]
we revealed a universal physical behaviour in the experimentally observed binding of two well-characterized NTRs,
\begin{align}
W^{(i)}(z) &= c^{(i)}(z) + V_{ext}^{(i)}(z) + \int \rho^{(3)}(z) u^{(i)}(z-z')\textrm{d}z' - \mu^{(i)} \nonumber, \\
& \approx - k_{\textrm{B}}T \ln \left( \frac{\rho^{(i)}(z)}{\rho^{(i)}_{\textrm{bulk}}} \right),
\end{align}
Was Further validated by a minimal physical model that treated the FG Nups as flexible homopolymers the NTRs as uniformly cohesive spheres.
\begin{align*}
W^{(i)}(z) &= c^{(i)}(z) + V_{ext}^{(i)}(z) + \int \rho^{(3)}(z) u^{(i)}(z-z')\textrm{d}z' - \mu^{(i)} \nonumber, \\
& \approx - k_{\textrm{B}}T \ln \left( \frac{\rho^{(i)}(z)}{\rho^{(i)}_{\textrm{bulk}}} \right),
\end{align*}
\end{document}
我的CFG
\Configure{ext}{xhtml}
\Preamble{xhtml,mathml,NLM,charset=UTF-8,-xtpipes,NoFonts,refcaption,ext=.xhtml}
\Configure{HtmlPar}{\EndP\HCode{<p class="noindent">}}
{\EndP\HCode{<p class="\ifdim\parindent=0pt no\fi indent">}}
{\HCode{</p>}}
{\HCode{</p>}}
\Configure{HTML}{\HCode{<html xmlns="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML">}}
{\HCode{</html>}}
\Configure{mathml}{mml:}
\Configure{MathClass}{0}{*}{<mml:mi>}{</mml:mi>}{}
\Configure{MathClass}{1}{*}{<mml:mo mmlclass="MathClass-op">}{</mml:mo>}{}
\Configure{MathClass}{2}{*}{<mml:mo mmlclass="MathClass-bin">}{</mml:mo>}{}
\Configure{MathClass}{3}{*}{<mml:mo mmlclass="MathClass-rel">}{</mml:mo>}{}
\Configure{MathClass}{4}{*}{<mml:mrow><mml:mo mmlclass="MathClass-open">}
{</mml:mo><mml:mrow>}{}
\Configure{MathClass}{5}{*}{</mml:mrow><mml:mo mmlclass="MathClass-close">}
{</mml:mo></mml:mrow>}{}
\Configure{MathClass}{6}{*}{<mml:mo mmlclass="MathClass-punc">}{</mml:mo>}{}
\Configure{MathClass}{7}{*}{<mml:mn>}{</mml:mn>}
{0123456789}
\newtoks\eqtoks
\ExplSyntaxOn
\cs_new_protected:Npn \alteqtoks #1
{
\tl_set:Nx \l_tmpa_tl {\detokenize{#1}}
% % replace < > and & with xml entities
\regex_replace_all:nnN { \x{26} } { & } \l_tmpa_tl
\regex_replace_all:nnN { \x{3C} } { < } \l_tmpa_tl
\regex_replace_all:nnN { \x{3E} } { > } \l_tmpa_tl
% replace \par command with blank lines
\regex_replace_all:nnN { \x{5C}par\b } {\x{A}\x{A}} \l_tmpa_tl
\tl_set:Nx \eqtoks{ \l_tmpa_tl }
%\HCode{\l_tmpb_tl}
}
\ExplSyntaxOff
\def\AltMath#1${\alteqtoks{#1}%
#1\HCode{</mrow><annotation encoding="application/x-tex">\eqtoks</annotation>}$}
\Configure{$}{\Configure{@math}{display="inline"}\DviMath\HCode{<semantics><mrow>}}{\HCode{</semantics>}\EndDviMath}{\expandafter\AltMath}
\long\def\AltDisplay#1\]{\alteqtoks{#1}#1\HCode{</mrow><annotation encoding="application/x-tex">\eqtoks</annotation></semantics>}\]}
\Configure{[]}{\Configure{@math}{display="block"}\DviMath$$\DisplayMathtrue\HCode{<semantics><mrow>}\AltDisplay}{$$\EndDviMath}
\renewcommand\eqannotate[1]{\alteqtoks{#1}\HCode{<semantics><mrow>}#1\HCode{</mrow><annotation encoding="application/x-tex">\eqtoks</annotation></semantics>}}
% environment support
\newcommand\VerbMathToks[2]{%
\alteqtoks{\begin{#2}
#1
\end{#2}}%
\ifvmode\IgnorePar\fi\EndP\Configure{@math}{display="block"}\DviMath\DisplayMathtrue\HCode{<semantics><mrow>}
\begin{old#2}
#1
\end{old#2}
\HCode{</mrow><annotation encoding="application/x-tex">}
\HCode{\eqtoks}
\HCode{</annotation></semantics>}
\EndDviMath
}
\ExplSyntaxOn
\newcommand\VerbMath[1]{%
\cs_if_exist:cTF{#1}{
\expandafter\let\csname old#1\expandafter\endcsname\csname #1\endcsname
\expandafter\let\csname endold#1\expandafter\endcsname\csname end#1\endcsname
\RenewDocumentEnvironment{#1}{+!b}{%
\NoFonts\expandafter\VerbMathToks\expandafter{##1}{#1}\EndNoFonts%
}{}
}{}%
}
\ExplSyntaxOff
\begin{document}
\VerbMath{aligned}
\VerbMath{alignedat}
\VerbMath{gather}
\VerbMath{gather*}
\VerbMath{alignat}
\VerbMath{alignat*}
\VerbMath{xalignat}
\VerbMath{xalignat*}
\VerbMath{xxalignat}
\VerbMath{align}
\VerbMath{align*}
\VerbMath{flalign}
\VerbMath{flalign*}
\VerbMath{multline}
\VerbMath{multline*}
\VerbMath{equation}
\VerbMath{equation*}
\VerbMath{math}
\VerbMath{displaymath}
\VerbMath{eqnarray}
\VerbMath{eqnarray*}
\EndPreamble
答案1
我将基于较新的答案。第二个似乎过时了。它只需要修复方程式,它们会导致编译错误。除此之外,它大部分都有效。除了$$ ... $$
数学,我找不到正确的解决方案。
这是更新后的配置文件:
\Preamble{xhtml,mathml,mathjax}
\newtoks\eqtoks
\ExplSyntaxOn
\cs_new_protected:Npn \alteqtoks #1
{
\tl_set:Nx \l_tmpa_tl {\detokenize{#1}}
% % replace < > and & with xml entities
\regex_replace_all:nnN { \x{26} } { & } \l_tmpa_tl
\regex_replace_all:nnN { \x{3C} } { < } \l_tmpa_tl
\regex_replace_all:nnN { \x{3E} } { > } \l_tmpa_tl
% replace \par command with blank lines
\regex_replace_all:nnN { \x{5C}par\b } {\x{A}\x{A}} \l_tmpa_tl
\tl_set:Nx \eqtoks{ \l_tmpa_tl }
%\HCode{\l_tmpb_tl}
}
\ExplSyntaxOff
\def\AltMath#1${\alteqtoks{#1}%
#1\HCode{</mrow><annotation encoding="application/x-tex">\eqtoks</annotation>}$}
\Configure{$}{\Configure{@math}{display="inline"}\DviMath\HCode{<semantics><mrow>}}{\HCode{</semantics>}\EndDviMath}{\expandafter\AltMath}
\long\def\AltDisplay#1\]{\alteqtoks{#1}#1\HCode{</mrow><annotation encoding="application/x-tex">\eqtoks</annotation></semantics>}\]}
\Configure{[]}{\Configure{@math}{display="block"}\DviMath$$\DisplayMathtrue\HCode{<semantics><mrow>}\AltDisplay}{$$\EndDviMath}
\renewcommand\eqannotate[1]{\alteqtoks{#1}\HCode{<semantics><mrow>}#1\HCode{</mrow><annotation encoding="application/x-tex">\eqtoks</annotation></semantics>}}
% environment support
\newcommand\VerbMathToks[2]{%
\alteqtoks{\begin{#2}
#1
\end{#2}}%
\begingroup%
\ifvmode\IgnorePar\fi\EndP\Configure{@math}{display="block"}\DviMath\DisplayMathtrue\HCode{<semantics><mrow>}
\Configure{$$}{}{}{}
\begin{old#2}
#1
\end{old#2}
\HCode{</mrow><annotation encoding="application/x-tex">}
\HCode{\eqtoks}
\HCode{</annotation></semantics>}
\EndDviMath
\endgroup
}
\makeatletter
% we must handle equations separatelly.
% it is a bit messy
\newcommand\VerbMathToksEquation[2]{%
\alteqtoks{\begin{#2}
#1
\end{#2}}%
\begingroup%
\def\@tempa{#2}%
\def\@equationname{equation}%
\def\mlabeledtr{mtr}
\ifx\@equationname\@tempa%
\def\mlabeledtr{mlabeledtr} % this element can be used to print the equation number, but it is supported only by MathJax
\fi
\ifvmode\IgnorePar\fi\EndP\Configure{@math}{display="block"}\DviMath\DisplayMathtrue\HCode{<semantics><mrow><mtable><\mlabeledtr><mtd>}%
\ifx\@equationname\@tempa%
\incr@eqnum%
\print@eqnum%
\HCode{</mtd><mtd>}%
\fi
#1%
\HCode{</mtd></\mlabeledtr></mtable></mrow><annotation encoding="application/x-tex">}%
\HCode{\eqtoks}%
\HCode{</annotation></semantics>}%
\EndDviMath%
\endgroup%
}
\makeatother
\ExplSyntaxOn
\newcommand\VerbMath[1]{%
\cs_if_exist:cTF{#1}{
\expandafter\let\csname old#1\expandafter\endcsname\csname #1\endcsname
\expandafter\let\csname endold#1\expandafter\endcsname\csname end#1\endcsname
\RenewDocumentEnvironment{#1}{+!b}{%
\NoFonts\expandafter\VerbMathToks\expandafter{##1}{#1}\EndNoFonts%
}{}
}{}%
}
\newcommand\VerbEquation[1]{%
\cs_if_exist:cTF{#1}{
\expandafter\let\csname old#1\expandafter\endcsname\csname #1\endcsname
\expandafter\let\csname endold#1\expandafter\endcsname\csname end#1\endcsname
\RenewDocumentEnvironment{#1}{+!b}{%
\NoFonts\expandafter\VerbMathToksEquation\expandafter{##1}{#1}\EndNoFonts%
}{}
}{}%
}
\ExplSyntaxOff
\begin{document}
\VerbMath{subarray}
\VerbMath{smallmatrix}
\VerbMath{matrix}
\VerbMath{pmatrix}
\VerbMath{bmatrix}
\VerbMath{Bmatrix}
\VerbMath{vmatrix}
\VerbMath{Vmatrix}
\VerbMath{cases}
\VerbMath{subequations}
\VerbMath{aligned}
\VerbMath{alignedat}
\VerbMath{gathered}
\VerbMath{gather}
\VerbMath{gather*}
\VerbMath{alignat}
\VerbMath{alignat*}
\VerbMath{xalignat}
\VerbMath{xalignat*}
\VerbMath{xxalignat}
\VerbMath{align}
\VerbMath{align*}
\VerbMath{flalign}
\VerbMath{flalign*}
\VerbMath{split}
\VerbMath{multline}
\VerbMath{multline*}
\VerbEquation{equation}
\VerbEquation{equation*}
\VerbMath{math}
\VerbMath{displaymath}
\VerbMath{eqnarray}
\VerbMath{eqnarray*}
\EndPreamble
结果如下:
<!DOCTYPE html>
<html lang='en-US' xml:lang='en-US'>
<head> <title></title>
<meta charset='utf-8' />
<meta content='TeX4ht (https://tug.org/tex4ht/)' name='generator' />
<meta content='width=device-width,initial-scale=1' name='viewport' />
<link href='sample.css' rel='stylesheet' type='text/css' />
<meta content='sample.tex' name='src' />
<script async='async' id='MathJax-script' src='https://cdn.jsdelivr.net/npm/mathjax@3/es5/mml-chtml.js' type='text/javascript'></script>
</head><body>
<!-- l. 10 --><p class='noindent'>Inline math <!-- l. 10 --><math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mi>a</mi> <mo class='MathClass-bin' stretchy='false'>+</mo> <mi>b</mi> <mo class='MathClass-rel' stretchy='false'>=</mo> <mi>c</mi></mrow><annotation encoding='application/x-tex'>a+b=c</annotation></semantics></math>
</p><!-- l. 12 --><p class='indent'> Display equation with doble dollar
<!-- tex4ht:inline --></p><!-- l. 13 --><math display='block' xmlns='http://www.w3.org/1998/Math/MathML'><mrow>
<mi>a</mi> <mo class='MathClass-bin' stretchy='false'>+</mo> <mi>b</mi> <mo class='MathClass-rel' stretchy='false'>=</mo> <mi>c</mi>
</mrow></math>
<!-- l. 15 --><p class='nopar'>
</p><!-- l. 18 --><p class='indent'> <!-- l. 18 --><math display='block' xmlns='http://www.w3.org/1998/Math/MathML'><mrow>
<semantics><mrow><mi>a</mi> <mo class='MathClass-bin' stretchy='false'>+</mo> <mi>b</mi> <mo class='MathClass-rel' stretchy='false'>=</mo> <mi>c</mi></mrow><annotation encoding='application/x-tex'> a+b=c </annotation></semantics>
</mrow></math>
</p><!-- l. 22 --><p class='indent'> Display equation (equation env) </p><!-- l. 25 --><math display='block' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mtable><mlabeledtr><mtd><mstyle class='label' id='x1-2r1'></mstyle><!-- endlabel --><mstyle class='maketag'><mtext>(1)</mtext></mstyle><mspace class='nbsp' width='0.33em'></mspace></mtd><mtd> <mi>x</mi><mo class='MathClass-bin' stretchy='false'>+</mo><mi>y</mi><mo class='MathClass-rel' stretchy='false'>=</mo><mn>1</mn> </mtd></mlabeledtr></mtable></mrow><annotation encoding='application/x-tex'>\begin {equation} x+y=1 \end {equation}</annotation></semantics></math>
<!-- l. 27 --><p class='indent'> Display equation (equation* env) </p><!-- l. 30 --><math display='block' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mtable><mtr><mtd> <mi>x</mi><mo class='MathClass-bin' stretchy='false'>+</mo><mi>y</mi><mo class='MathClass-rel' stretchy='false'>=</mo><mi>z</mi> </mtd></mtr></mtable></mrow><annotation encoding='application/x-tex'>\begin {equation*} x+y=z \end {equation*}</annotation></semantics></math>
<!-- l. 32 --><p class='indent'> eqnarray environment </p><!-- l. 35 --><math display='block' xmlns='http://www.w3.org/1998/Math/MathML'><mrow><semantics><mrow>
<mtable class='eqnarray' columnalign='right center left' displaystyle='true'>
<mtr><mtd class='eqnarray-1'> <mi>x</mi> <mo class='MathClass-bin' stretchy='false'>+</mo> <mi>y</mi> <mo class='MathClass-rel' stretchy='false'>=</mo> <mn>1</mn></mtd><mtd class='eqnarray-2'> </mtd><mtd class='eqnarray-3'> </mtd><mtd class='eqnarray-4'> <mtext class='eqnarray'>(2)</mtext><mtext class='label' id='x1-3r'></mtext><mtext class='endlabel'></mtext></mtd> </mtr></mtable>
</mrow><annotation encoding='application/x-tex'> \begin {eqnarray} x+y=1 \end {eqnarray} </annotation></semantics> </mrow></math>
<!-- l. 37 --><p class='indent'> display equation <!-- l. 38 --><math display='block' xmlns='http://www.w3.org/1998/Math/MathML'><mrow>
<semantics><mrow><mi>d</mi> <mo class='MathClass-bin' stretchy='false'>+</mo> <mi>f</mi> <mo class='MathClass-rel' stretchy='false'>=</mo> <mi>g</mi></mrow><annotation encoding='application/x-tex'> d+f=g </annotation></semantics>
</mrow></math>
</p><!-- l. 42 --><p class='indent'> we revealed a universal physical behaviour in the
experimentally observed binding of two well-characterized NTRs,
</p><!-- l. 46 --><math display='block' xmlns='http://www.w3.org/1998/Math/MathML'><mrow><semantics><mrow>
<!-- tex4ht:inline --><mrow><mtable class='align' columnalign='left' displaystyle='true'>
<mtr><mtd class='align-odd' columnalign='right'><msup><mrow><mi>W</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi><mo class='MathClass-close' stretchy='false'>)</mo></mtd> <mtd class='align-even'> <mo class='MathClass-rel' stretchy='false'>=</mo> <msup><mrow><mi>c</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi><mo class='MathClass-close' stretchy='false'>)</mo> <mo class='MathClass-bin' stretchy='false'>+</mo> <msubsup><mrow><mi>V</mi> </mrow><mrow>
<mi mathvariant='italic'>ext</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msubsup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi><mo class='MathClass-close' stretchy='false'>)</mo> <mo class='MathClass-bin' stretchy='false'>+</mo><mo> ∫
<!-- nolimits --></mo><!-- nolimits --><msup><mrow><mi>ρ</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mn>3</mn><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi><mo class='MathClass-close' stretchy='false'>)</mo><msup><mrow><mi>u</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi> <mo class='MathClass-bin' stretchy='false'>−</mo> <msup><mrow><mi>z</mi></mrow><mrow><mi>′</mi></mrow></msup><mo class='MathClass-close' stretchy='false'>)</mo><mstyle class='text'><mtext class='textrm' mathvariant='normal'>d</mtext></mstyle><msup><mrow><mi>z</mi></mrow><mrow><mi>′</mi></mrow></msup><mo class='MathClass-bin' stretchy='false'>−</mo> <msup><mrow><mi>μ</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-punc' stretchy='false'>,</mo><mspace width='2em'></mspace></mtd> <mtd class='align-label' columnalign='right'></mtd> <mtd class='align-label'>
<mspace width='2em'></mspace></mtd></mtr><mtr><mtd class='align-odd' columnalign='right'></mtd> <mtd class='align-even'> <mo class='MathClass-rel' stretchy='false'>≈</mo><mo class='MathClass-bin' stretchy='false'>−</mo><msub><mrow><mi>k</mi></mrow><mrow><mstyle class='text'><mtext class='textrm' mathvariant='normal'>B</mtext></mstyle></mrow></msub><mi>T</mi><mi class='qopname'>ln</mi><mo> <!-- FUNCTION APPLICATION --> </mo><!-- nolimits --> <mrow><mo fence='true' form='prefix'> (</mo><mrow> <mfrac><mrow><msup><mrow><mi>ρ</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow>
<mrow><msubsup><mrow><mi>ρ</mi></mrow><mrow><mstyle class='text'><mtext class='textrm' mathvariant='normal'>bulk</mtext></mstyle></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msubsup></mrow></mfrac> </mrow><mo fence='true' form='postfix'>)</mo></mrow> <mo class='MathClass-punc' stretchy='false'>,</mo><mspace width='2em'></mspace></mtd> <mtd class='align-label' columnalign='right'><mstyle class='label' id='x1-4r3'></mstyle><!-- endlabel --><mstyle class='maketag'><mtext>(3)</mtext></mstyle><mspace class='nbsp' width='0.33em'></mspace> </mtd></mtr></mtable></mrow>
</mrow><annotation encoding='application/x-tex'> \begin {align} W^{(i)}(z) &= c^{(i)}(z) + V_{ext}^{(i)}(z) + \int \rho ^{(3)}(z) u^{(i)}(z-z')\textrm {d}z' - \mu ^{(i)} \nonumber , \\ & \approx - k_{\textrm {B}}T \ln \left ( \frac {\rho ^{(i)}(z)}{\rho ^{(i)}_{\textrm {bulk}}} \right ), \end {align} </annotation></semantics> </mrow></math>
<!-- l. 48 --><p class='noindent'>Was Further validated by a minimal physical model that treated the FG
Nups as flexible homopolymers the NTRs as uniformly cohesive spheres.
</p><!-- l. 52 --><math display='block' xmlns='http://www.w3.org/1998/Math/MathML'><mrow><semantics><mrow>
<!-- tex4ht:inline --><mrow><mtable class='align-star' columnalign='left' displaystyle='true'>
<mtr><mtd class='align-odd' columnalign='right'><msup><mrow><mi>W</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi><mo class='MathClass-close' stretchy='false'>)</mo></mtd> <mtd class='align-even'> <mo class='MathClass-rel' stretchy='false'>=</mo> <msup><mrow><mi>c</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi><mo class='MathClass-close' stretchy='false'>)</mo> <mo class='MathClass-bin' stretchy='false'>+</mo> <msubsup><mrow><mi>V</mi> </mrow><mrow>
<mi mathvariant='italic'>ext</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msubsup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi><mo class='MathClass-close' stretchy='false'>)</mo> <mo class='MathClass-bin' stretchy='false'>+</mo><mo> ∫
<!-- nolimits --></mo><!-- nolimits --><msup><mrow><mi>ρ</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mn>3</mn><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi><mo class='MathClass-close' stretchy='false'>)</mo><msup><mrow><mi>u</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi> <mo class='MathClass-bin' stretchy='false'>−</mo> <msup><mrow><mi>z</mi></mrow><mrow><mi>′</mi></mrow></msup><mo class='MathClass-close' stretchy='false'>)</mo><mstyle class='text'><mtext class='textrm' mathvariant='normal'>d</mtext></mstyle><msup><mrow><mi>z</mi></mrow><mrow><mi>′</mi></mrow></msup><mo class='MathClass-bin' stretchy='false'>−</mo> <msup><mrow><mi>μ</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-punc' stretchy='false'>,</mo><mspace width='2em'></mspace></mtd> <mtd class='align-label' columnalign='right'></mtd> <mtd class='align-label'>
<mspace width='2em'></mspace></mtd></mtr><mtr><mtd class='align-odd' columnalign='right'></mtd> <mtd class='align-even'> <mo class='MathClass-rel' stretchy='false'>≈</mo><mo class='MathClass-bin' stretchy='false'>−</mo><msub><mrow><mi>k</mi></mrow><mrow><mstyle class='text'><mtext class='textrm' mathvariant='normal'>B</mtext></mstyle></mrow></msub><mi>T</mi><mi class='qopname'>ln</mi><mo> <!-- FUNCTION APPLICATION --> </mo><!-- nolimits --> <mrow><mo fence='true' form='prefix'> (</mo><mrow> <mfrac><mrow><msup><mrow><mi>ρ</mi></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msup><mo class='MathClass-open' stretchy='false'>(</mo><mi>z</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow>
<mrow><msubsup><mrow><mi>ρ</mi></mrow><mrow><mstyle class='text'><mtext class='textrm' mathvariant='normal'>bulk</mtext></mstyle></mrow><mrow><mo class='MathClass-open' stretchy='false'>(</mo><mi>i</mi><mo class='MathClass-close' stretchy='false'>)</mo></mrow></msubsup></mrow></mfrac> </mrow><mo fence='true' form='postfix'>)</mo></mrow> <mo class='MathClass-punc' stretchy='false'>,</mo><mspace width='2em'></mspace></mtd> <mtd class='align-label' columnalign='right'></mtd> <mtd class='align-label'><mspace width='2em'></mspace></mtd></mtr></mtable></mrow>
</mrow><annotation encoding='application/x-tex'> \begin {align*} W^{(i)}(z) &= c^{(i)}(z) + V_{ext}^{(i)}(z) + \int \rho ^{(3)}(z) u^{(i)}(z-z')\textrm {d}z' - \mu ^{(i)} \nonumber , \\ & \approx - k_{\textrm {B}}T \ln \left ( \frac {\rho ^{(i)}(z)}{\rho ^{(i)}_{\textrm {bulk}}} \right ), \end {align*} </annotation></semantics> </mrow></math>
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