# 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.

•  $\mathchoice{{\vbox{\hbox{\textstyle=}}\kern-7.499886pt}}{{\vbox{\hbox{% \scriptstyle=}}\kern-6.374903pt}}{{\vbox{\hbox{\scriptscriptstyle=}}\kern-4% .499931pt}}{{\vbox{\hbox{\scriptscriptstyle=}}\kern-3.749943pt}}\!\int_{% \Omega}F(\zeta,\eta)d\zeta d\eta$
•  $\mathchoice{{\vbox{\hbox{\textstyle-}}\kern-7.499886pt}}{{\vbox{\hbox{% \scriptstyle-}}\kern-6.374903pt}}{{\vbox{\hbox{\scriptscriptstyle-}}\kern-4% .499931pt}}{{\vbox{\hbox{\scriptscriptstyle-}}\kern-3.749943pt}}\!\int_{z_{0% }}^{z}f(\zeta)d\zeta$
•  $Ei(z)=-\mathchoice{{\vbox{\hbox{\textstyle-}}\kern-7.499886pt}}{{\vbox{\hbox% {\scriptstyle-}}\kern-6.374903pt}}{{\vbox{\hbox{\scriptscriptstyle-}}\kern% -4.499931pt}}{{\vbox{\hbox{\scriptscriptstyle-}}\kern-3.749943pt}}\!\int_{-z% }^{\infty}\frac{e^{-\zeta}}{\zeta}d\zeta=\mathchoice{{\vbox{\hbox{\textstyle-% }}\kern-7.499886pt}}{{\vbox{\hbox{\scriptstyle-}}\kern-6.374903pt}}{{\vbox{% \hbox{\scriptscriptstyle-}}\kern-4.499931pt}}{{\vbox{\hbox{% \scriptscriptstyle-}}\kern-3.749943pt}}\!\int_{-\infty}^{z}\frac{e^{\zeta}}{% \zeta}d\zeta,\quad\Re{z}>0,\quad\text{(exponential integral)}$
•  $li(z)=\mathchoice{{\vbox{\hbox{\textstyle-}}\kern-7.499886pt}}{{\vbox{\hbox{% \scriptstyle-}}\kern-6.374903pt}}{{\vbox{\hbox{\scriptscriptstyle-}}\kern-% 4.499931pt}}{{\vbox{\hbox{\scriptscriptstyle-}}\kern-3.749943pt}}\!\int_{0}^% {z}\frac{d\zeta}{\log\zeta}\equiv Ei(\log z),\;\Re{z}>1,\quad\text{(% logarithmic integral)}$
•  $\Gamma(z)\Gamma(1-z)=-z\Gamma(-z)\Gamma(z)=\mathchoice{{\vbox{\hbox{% \textstyle-}}\kern-7.499886pt}}{{\vbox{\hbox{\scriptstyle-}}\kern-6.374903% pt}}{{\vbox{\hbox{\scriptscriptstyle-}}\kern-4.499931pt}}{{\vbox{\hbox{% \scriptscriptstyle-}}\kern-3.749943pt}}\!\int_{0}^{\infty}\frac{\zeta^{z-1}}{% \zeta+1}d\zeta=\pi\csc\pi z,\quad 0<\Re{z}<1,\quad\text{(Gamma function % reflection's formula)}$
Title LaTeXsymbol for Cauchy principal value LaTeXSymbolForCauchyPrincipalValue 2013-03-22 17:49:51 2013-03-22 17:49:51 perucho (2192) perucho (2192) 5 perucho (2192) Feature msc 00A99 LogarithmicIntegral2