Symbol for repeated applications of an associative binary operation?

Question

I'd like to create a symbol do deal with repeated applications of an arbitrary associative operation *. Something like:

But this is not good looking to me. The proportions on the left hand doesn't pleases me.

Does anyone have any idea on how to improve it?

Thanks.

Answer 1

The solution in https://tex.stackexchange.com/a/306593/4427 can actually be used for all symbols that already lack a “big” version.

\documentclass{article}
\usepackage{graphicx}
\usepackage{amsmath}

\makeatletter
\newcommand{\bigsymbol}[1]{%
  \DOTSB
  \mathop{% we want it to be an operator
    \mathchoice{\big@symbol\displaystyle\Large{#1}}
               {\big@symbol\textstyle\large{#1}}
               {\big@symbol\scriptstyle\normalsize{#1}}
               {\big@symbol\scriptscriptstyle\small{#1}}%
    }\slimits@
}

\newcommand{\big@symbol}[3]{%
  \vcenter{%
    \sbox\z@{$#1\sum$}%
    \dimen@=0.875\dimexpr\ht\z@+\dp\z@\relax
    #2% font size
    \hbox{\resizebox{!}{\dimen@}{$\m@th#3$}}%
  }%
  \vphantom{\sum}%
}
\makeatother

\newcommand{\bigast}{\bigsymbol{*}}

\begin{document}
Here's in text, $\bigast_{i=1}^n x_i$, next in display
\[
\bigast_{i=1}^n x_i=x_1*x_2*\dots*x_n
\]
\end{document}

Answer 2

not as general as the one egreg just posted, but simpler:-)

\documentclass{article}

\usepackage{amsmath}

\newcommand\bigast{\mathop{\mathchoice{\hbox{\large$\ast$}}{\ast}{\scriptstyle\ast}{\scriptscriptstyle\ast}}}

\begin{document}

\[\bigast_{i=1}^n x_i = x_1\ast\dots\ast x_n\]


$\bigast_{i=1}^n x_i = x_1\ast\dots\ast x_n$

\end{document}