Regularized Product Symbol

Question

How so I make a regularized product symbol like in Deninger's papers. It looks like a II, only large like $\prod$ only with a bottom on it too, as in the following paper abstract:

Answer 1

Here's a definition that will produce the proper size and the proper placement of the limits depending on the mode; I also provided a tentative definition for the dotted product and the double-dotted product:

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

\DeclareMathOperator*\Rprod{%
\mathchoice
  {\ooalign{$\displaystyle\prod$\cr\hidewidth$\displaystyle\coprod$\hidewidth\cr}}%
  {\ooalign{$\textstyle\prod$\cr\hidewidth$\textstyle\coprod$\hidewidth\cr}}%
  {\ooalign{$\scriptstyle\prod$\cr\hidewidth$\scriptstyle\coprod$\hidewidth\cr}}%
  {\ooalign{$\scriptscriptstyle\prod$\cr\hidewidth$%
  \scriptscriptstyle\coprod$\hidewidth\cr}}}

\DeclareMathOperator*\Dprod{%
\mathchoice
  {\ooalign{$\bullet$\cr\hidewidth$\displaystyle\Rprod$\hidewidth\cr}}%
  {\ooalign{\scalebox{.7}{$\bullet$}\cr\hidewidth$\textstyle\Rprod$\hidewidth\cr}\mkern6mu}%
  {\mkern6mu\ooalign{\scalebox{.6}{$\bullet$}\cr\hidewidth$\scriptstyle\Rprod$\hidewidth\cr}\mkern3mu}%
  {\mkern4mu\ooalign{\scalebox{.5}{$\bullet$}\cr\hidewidth$\scriptscriptstyle\Rprod$\hidewidth\cr}\mkern2mu}}

\newcommand\Vbullet{\raisebox{-2.1pt}{\kern-0.4pt\vbox{\baselineskip4pt\lineskiplimit0pt%
\hbox{$\bullet$}\hbox{$\bullet$}}}}

\DeclareMathOperator*\DDprod{%
\mathchoice
  {\ooalign{$\Vbullet$\cr\hidewidth$\displaystyle\Rprod$\hidewidth\cr}}%
  {\ooalign{\scalebox{.7}{$\Vbullet$}\cr\hidewidth$\textstyle\Rprod$\hidewidth\cr}\mkern6mu}%
  {\mkern6mu\ooalign{\scalebox{.6}{$\Vbullet$}\cr\hidewidth$\scriptstyle\Rprod$\hidewidth\cr}\mkern3mu}%
  {\mkern4mu\ooalign{\scalebox{.5}{$\Vbullet$}\cr\hidewidth$\scriptscriptstyle\Rprod$\hidewidth\cr}\mkern2mu}}

\begin{document}

\[
  \Rprod_{n\in I}a_{n}  
\]
$\Rprod_{n\in I}a_{n}$
\[
\Dprod_{n\in I}a_{n}
\]
$\Dprod_{n\in I}a_{n}$
\[
\DDprod_{n\in I}a_{n}
\]
$\DDprod_{n\in I}a_{n}$

\end{document}

Answer 2

Maybe a better solution inspired by Gonzalo's

\documentclass{article}
\usepackage{amsmath}

\def\doubleprod#1#2{\ooalign{$#1\prod$\cr$#1\coprod$\cr}}
\def\ddoubleprod#1#2{\ooalign{\hidewidth$#1\onebullet$\hidewidth\cr$#1\Rprod$\cr}}
\def\dddoubleprod#1#2{\ooalign{\hidewidth$#1\twobullets$\hidewidth\cr$#1\Rprod$\cr}}
\def\onebullet{\mathchoice
  {\vcenter{\hbox{$\bullet$}}}
  {\vcenter{\hbox{$\scriptstyle\bullet$}}}
  {\vcenter{\hbox{$\scriptscriptstyle\bullet$}}}
  {\vcenter{\hbox{$\cdot$}}}
}
\def\twobullets{\mathchoice
  {\vcenter{\offinterlineskip\hbox{$\bullet$}\kern.2ex\hbox{$\bullet$}}}
  {\vcenter{\offinterlineskip\hbox{$\scriptstyle\bullet$}\kern.2ex\hbox{$\scriptstyle\bullet$}}}
  {\vcenter{\offinterlineskip\hbox{$\scriptscriptstyle\bullet$}\kern.1ex\hbox{$\scriptscriptstyle\bullet$}}}
  {\vcenter{\offinterlineskip\hbox{$\cdot$}\kern-1.4ex\hbox{$\cdot$}}}
}

\DeclareMathOperator*{\Rprod}{\mathpalette\doubleprod\relax}
\DeclareMathOperator*\Dprod{\mathpalette\ddoubleprod\relax}
\DeclareMathOperator*\DDprod{\mathpalette\dddoubleprod\relax}

\begin{document}

$\displaystyle\prod_{n\in I}\Rprod_{n\in I}a_{n}X_{\Rprod_{\Rprod}}\textstyle\Rprod$

$\displaystyle\prod_{n\in I}\Dprod_{n\in I}a_{n}X_{\Dprod_{\Dprod}}\textstyle\Dprod$

$\displaystyle\prod_{n\in I}\DDprod_{n\in I}a_{n}X_{\DDprod_{\DDprod}}\textstyle\DDprod$

\end{document}

The \prod are only to check for proper alignment of the subscript.

If you need only the symbol shown in the first line, then

\def\doubleprod#1#2{\ooalign{$#1\prod$\cr$#1\coprod$\cr}}
\DeclareMathOperator*{\Rprod}{\mathpalette\doubleprod\relax}

is sufficient.

Answer 3

Here is one way to do it:

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{mathtools}
\DeclareMathOperator{\MyProd}{\scalebox{1.4}{$\mathrm{I\kern-0.2ex I}$}}

\begin{document}
$\prod  $ \quad\verb|\prod|

$\MyProd$ \quad\verb|\MyProd|
\end{document}