LaTeXsymbol for Cauchy principal value

The usual symbol (dashed integral) used to denote Cauchy’s principal value of an integral can be created in LaTeX through macros.¹¹UK List of TeX is a reference. These one are given by the following instructions, which must be included on the preamble.

\def\Xint#1{\mathchoice
   {\XXint\displaystyle\textstyle{#1}}%
   {\XXint\textstyle\scriptstyle{#1}}%
   {\XXint\scriptstyle\scriptscriptstyle{#1}}%
   {\XXint\scriptscriptstyle\scriptscriptstyle{#1}}%
   \!\int}
\def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$}
     \vcenter{\hbox{$#2#3$}}\kern-.5\wd0}}
\def\ddashint{\Xint=}
\def\dashint{\Xint-}

The commands to execute those macros are $``\backslash dashint"$ and $``\backslash ddashint"$ for single dash and double dash, respectively. Let us expose a few examples.

•

$\mathchoice{{\vbox{\hbox{$\textstyle=$}}\kern-7.499886pt}}{{\vbox{\hbox{$% \scriptstyle=$}}\kern-6.374903pt}}{{\vbox{\hbox{$\scriptscriptstyle=$}}\kern-4% .499931pt}}{{\vbox{\hbox{$\scriptscriptstyle=$}}\kern-3.749943pt}}\!\int_{% \Omega}F(\zeta,\eta)d\zeta d\eta$
•

$\mathchoice{{\vbox{\hbox{$\textstyle-$}}\kern-7.499886pt}}{{\vbox{\hbox{$% \scriptstyle-$}}\kern-6.374903pt}}{{\vbox{\hbox{$\scriptscriptstyle-$}}\kern-4% .499931pt}}{{\vbox{\hbox{$\scriptscriptstyle-$}}\kern-3.749943pt}}\!\int_{z_{0% }}^{z}f(\zeta)d\zeta$
•

$Ei(z)=-\mathchoice{{\vbox{\hbox{$\textstyle-$}}\kern-7.499886pt}}{{\vbox{\hbox% {$\scriptstyle-$}}\kern-6.374903pt}}{{\vbox{\hbox{$\scriptscriptstyle-$}}\kern% -4.499931pt}}{{\vbox{\hbox{$\scriptscriptstyle-$}}\kern-3.749943pt}}\!\int_{-z% }^{\infty}\frac{e^{-\zeta}}{\zeta}d\zeta=\mathchoice{{\vbox{\hbox{$\textstyle-% $}}\kern-7.499886pt}}{{\vbox{\hbox{$\scriptstyle-$}}\kern-6.374903pt}}{{\vbox{% \hbox{$\scriptscriptstyle-$}}\kern-4.499931pt}}{{\vbox{\hbox{$% \scriptscriptstyle-$}}\kern-3.749943pt}}\!\int_{-\infty}^{z}\frac{e^{\zeta}}{% \zeta}d\zeta,\quad\Re{z}>0,\quad\text{(exponential integral)}$
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$li(z)=\mathchoice{{\vbox{\hbox{$\textstyle-$}}\kern-7.499886pt}}{{\vbox{\hbox{% $\scriptstyle-$}}\kern-6.374903pt}}{{\vbox{\hbox{$\scriptscriptstyle-$}}\kern-% 4.499931pt}}{{\vbox{\hbox{$\scriptscriptstyle-$}}\kern-3.749943pt}}\!\int_{0}^% {z}\frac{d\zeta}{\log\zeta}\equiv Ei(\log z),\;\Re{z}>1,\quad\text{(% logarithmic integral)}$
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$\Gamma(z)\Gamma(1-z)=-z\Gamma(-z)\Gamma(z)=\mathchoice{{\vbox{\hbox{$% \textstyle-$}}\kern-7.499886pt}}{{\vbox{\hbox{$\scriptstyle-$}}\kern-6.374903% pt}}{{\vbox{\hbox{$\scriptscriptstyle-$}}\kern-4.499931pt}}{{\vbox{\hbox{$% \scriptscriptstyle-$}}\kern-3.749943pt}}\!\int_{0}^{\infty}\frac{\zeta^{z-1}}{% \zeta+1}d\zeta=\pi\csc\pi z,\quad 0<\Re{z}<1,\quad\text{(Gamma function % reflection's formula)}$

Title	LaTeXsymbol for Cauchy principal value
Canonical name	LaTeXSymbolForCauchyPrincipalValue
Date of creation	2013-03-22 17:49:51
Last modified on	2013-03-22 17:49:51
Owner	perucho (2192)
Last modified by	perucho (2192)
Numerical id	5
Author	perucho (2192)
Entry type	Feature
Classification	msc 00A99
Related topic	LogarithmicIntegral2