Symbols – How to Arc Center Dots Between Factors for Repeated Multiplication

Question

Consider the center dots to show repeated multiplication:

\[
x \cdot x \cdot x \cdots x.
\]

I want to use five dots instead of the three from the \cdots command, and I also want to have them subtly arced like on the path of part of a downward-opening parabola or something.

Does such a command already exist? If not, is it possible to create such a command or achieve it on a one-off/as-needed basis?

pdfLaTeX user.

Answer 1

If the horizontal spacing needs changing, that can be done with kerns. If it is needed in smaller (script) mathstyles, let me know in a comment and I will revise my answer to provide them.

\documentclass[10pt]{article}
\usepackage{amsmath}
\newcommand\repdots{\mathbin{{\cdot}\raisebox{.75pt}{$\cdot$}%
  \raisebox{1pt}{$\cdot$}\raisebox{.75pt}{$\cdot$}{\cdot}}}
\begin{document}
$x \cdot x \cdot x \cdots x.$

$x \cdot x \cdot x  \repdots x.$
\end{document}

SUPPLEMENT to add extra \cdot kern (also supports smaller mathstyles)

The value of \dotkern is used to space out the \cdots. The value 1\LMpt (Local Math pt) is 1 pt in text and display styles, but proportionately smaller in the smaller math styles.

\documentclass[10pt]{article}
\usepackage{amsmath,scalerel}
\newcommand\dotkern{\kern1\LMpt}
\newcommand\repdots{\mathbin{\ThisStyle{{\cdot}\dotkern%
  \raisebox{.75\LMpt}{$\SavedStyle\cdot$}\dotkern
  \raisebox{1\LMpt}{$\SavedStyle\cdot$}\dotkern%
  \raisebox{.75\LMpt}{$\SavedStyle\cdot$}\dotkern{\cdot}}}}
\begin{document}
$x \cdot x \cdot x \cdots x.$

$x \cdot x \cdot x  \repdots x.$

$\scriptstyle x \cdot x \cdot x  \repdots x.$

$\scriptscriptstyle x \cdot x \cdot x  \repdots x.$
\end{document}