Lowercase pi that is shown correctly in sub- and superscripts

Question

I am looking for a way to define a new mathematical symbol, namely a lowercase pi, that will resize according to the font size of the surrounding text. The normal \pi will not suffice as I am already using it to denote the constant 3.14... I am also using \varpi for something else. I was thinking that a lowercase version of \varPi, that is \scriptstyle \varPi, would work. Basically, I want something like:

and so on. It is important that the lower case pi looks like \scriptstyle \varPi because I am using it to denote a realization of a stochastic process denoted by \varPi.

Answer 1

This might be what you're looking for:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand{\smallPi}{\mathpalette\small@Pi\relax}
\newcommand{\small@Pi}[2]{%
  \mbox{\fontsize{\sf@size}{\z@}\selectfont$\m@th#1\varPi$}%
}
\makeatother

\begin{document}
\[
% first like it is in inline formulas
{\textstyle\smallPi x_{x\smallPi}}\qquad
% then in displays
\int_{\smallPi}
\]
\end{document}

The macro typesets \varPi at the size used for subscripts, but taking into account the current style.

Answer 2

This approach uses the scalerel package to scale the \varPI to the same vertical extent as an x in the local math style. Thus it automatically works for sub- and superscripts, as well as in all cases of \scriptstyle and \scriptscriptstyle.

\documentclass{article}
\usepackage{amsmath, scalerel}

\newcommand{\smallPi}{\scalerel*{\varPi}{x}}

\begin{document}
\[
% first like it is in inline formulas
{\textstyle\smallPi x_{x\smallPi}}\qquad
% then in displays
\int_{\smallPi} 
\]
\[
% first like it is in inline formulas
{\scriptstyle\smallPi x_{x\smallPi}}\qquad
% then in displays
\scriptstyle\int_{\smallPi} 
\]

\end{document}