Five iterated integrals

Question

Apparently, there are the commands \iint, \iiint, and \iiiint to type iterated integral symbols. To compute an integral in R^4 x [0,T] (i.e. over a 4-dimensional space and time), I would type \iiiiint_{\mathbb R^4 \times [0,T]}, except that the command \iiiiint is not pre-defined. Is there a way to type a symbol containing five iterated integrals?

Answer 1

The amsmath package already provides the infrastructure:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\ams@newcommand{\iiiiint}{\DOTSI\protect\MultiIntegral{5}}
\renewcommand{\MultiIntegral}[1]{%
  \edef\ints@c{\noexpand\intop
    \ifnum#1=\z@\noexpand\intdots@\else\noexpand\intkern@\fi
    \ifnum#1>\tw@\noexpand\intop\noexpand\intkern@\fi
    \ifnum#1>\thr@@\noexpand\intop\noexpand\intkern@\fi
    \ifnum#1>4 \noexpand\intop\noexpand\intkern@\fi % <---- added
    \noexpand\intop
    \noexpand\ilimits@
  }%
  \futurelet\@let@token\ints@a
}
\makeatother

\begin{document}
\begin{gather}
\int\quad
\iint\quad
\iiint\quad
\iiiint\quad
\iiiiint
\\
\int_{\Gamma}\quad
\iint_{\Gamma}\quad
\iiint_{\Gamma}\quad
\iiiint_{\Gamma}\quad
\iiiiint_{\Gamma}
\\
\int\limits_{\Gamma}\quad
\iint\limits_{\Gamma}\quad
\iiint\limits_{\Gamma}\quad
\iiiint\limits_{\Gamma}\quad
\iiiiint\limits_{\Gamma}
\end{gather}
\end{document}

A variant allowing any number of integral signs; \multiint should only be used with an argument at least 2.

\documentclass{article}
\usepackage{amsmath}
\usepackage{expl3}

\makeatletter
%\ams@newcommand{\iiiiint}{\DOTSI\protect\MultiIntegral{5}}
\ams@newcommand{\multiint}[1]{\DOTSI\protect\MultiIntegral{#1}}
\renewcommand{\MultiIntegral}[1]{%
  \edef\ints@c{\noexpand\intop
    \ifnum#1=\z@\noexpand\intdots@\else\noexpand\intkern@\fi
    \replicate{#1-2}{\noexpand\intop\noexpand\intkern@}%
    \noexpand\intop
    \noexpand\ilimits@
  }%
  \futurelet\@let@token\ints@a
}
\makeatother
\ExplSyntaxOn
\cs_new:Npn \replicate #1 #2 { \prg_replicate:nn { #1 } { #2 } }
\ExplSyntaxOff

\begin{document}
\begin{gather}
\int\quad
\iint\quad
\iiint\quad
\multiint{4}\quad
\multiint{5}\quad
\multiint{6}
\\
\int_{\Gamma}\quad
\iint_{\Gamma}\quad
\iiint_{\Gamma}\quad
\multiint{4}_{\Gamma}\quad
\multiint{5}_{\Gamma}\quad
\multiint{6}_{\Gamma}
\\
\int\limits_{\Gamma}\quad
\iint\limits_{\Gamma}\quad
\iiint\limits_{\Gamma}\quad
\multiint{4}\limits_{\Gamma}\quad
\multiint{5}\limits_{\Gamma}\quad
\multiint{6}\limits_{\Gamma}
\end{gather}
\end{document}