LaTeXsymbol for Cauchy principal value

The usual symbol (dashed integral) used to denote Cauchy’s principal value of an integral can be created inLaTeX through macros. 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     and    for single dash and double dash, respectively. Let us expose a few examples.

• $$={\int }_{\mathrm{\Omega }}F(\zeta ,\eta )𝑑\zeta 𝑑\eta$$

• $$-{\int }_{z_0}^{z}f(\zeta )𝑑\zeta$$

• $$Ei(z)=--{\int }_{-z}^{\mathrm{\infty }}\frac{e^{-\zeta }}{\zeta }d\zeta =-{\int }_{-\mathrm{\infty }}^z\frac{e^{\zeta }}{\zeta }d\zeta ,\mathrm{\Re }z>0,\text{(exponential integral)}$$

• $$li(z)=-{\int }_0^z\frac{d\zeta }{\log \zeta }\equiv Ei(\log z),\mathrm{\Re }z>1,\text{(logarithmic integral)}$$