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The usual symbol (dashed integral) used to denote Cauchy's principal value of an integral can be created in LATEX through macros.1 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.
- \begin{equation*}\ddashint_\Omega F(\zeta,\eta)d\zeta d\eta\end{equation*}
- \begin{equation*}\dashint_{z_0}^z f(\zeta)d\zeta\end{equation*}
- \begin{equation*}Ei(z)=-\dashint_{-z}^\infty \frac{e^{-\zeta}}{\zeta}d\zeta=\dashint_{-\infty}^z\frac{e^\zeta}{\zeta}d\zeta,\quad\Re{z}>0,\quad \text{(exponential integral)}\end{equation*}
- \begin{equation*}li(z)=\dashint_0^z\frac{d\zeta}{\log\zeta}\equiv Ei(\log z),\; \Re{z}>1,\quad \text{(logarithmic integral)}\end{equation*}
- \begin{equation*}\Gamma(z)\Gamma(1-z)=-z\Gamma(-z)\Gamma(z)=\dashint_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)}\end{equation*}
Footnotes
- 1
- UK List of TEX is a reference.
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