[Tex/LaTex] Multiple multiplication dots in a row

Question

What would be a correct way to write this (or is there another correct way)?
Thank you!!

    \documentclass[12pt]{article}

    \usepackage{amsmath,amsthm,amssymb,amsfonts}


    \begin{document}
    \begin{gather*}
        x_1\cdot x_2 \cdot \dotsm \cdot x_n \\
        x_1\cdot x_2 \cdot \dotsc \cdot x_n \\
        x_1\cdot x_2 \cdot\, \dotsm \,\cdot x_n
    \end{gather*}
    \end{document}

Answer 1

From the "The Chicago Manual of Style", 16th edition, paragraph 12.20:

If the multiplication dot is present, then ellipsis points should be on the baseline and not centered.

\documentclass[10pt]{article}
\usepackage{amsmath}

\begin{document}
$a_1\cdot a_2 \cdot\ldots\cdot a_n$\quad not\quad
$a_1\cdot a_2 \cdot\dots\cdot a_n$
\end{document}