Symbol for function composition like a big sum

Question

Coming from https://math.stackexchange.com/a/1097075/340174:

I would like to have something like

$$
\mathop{\bigcirc}^n_{k=0} f_k \quad \text{ or } \quad \mathop{\bigcirc}^0_{k=n} f_k
$$

but looking better - comparable in size and boldness to something like $\displaystyle\bigcap$ in $\displaystyle\bigcap_{k=0}^n A_k$ or to $\displaystyle\bigoplus$ .

How to do this?

Slightly off-topic: Don't use $$ for display math! Use \[ and \] instead. See Why is [ … ] preferable to $$ … $$?. — schtandard, Sep 22 '19 at 13:29
@schtandard: Thanks. In my LaTeX document I use equation and align environments and $. I used $$ just for tex.stackexchange.com. I guess $ is fine, right? — Make42, Sep 23 '19 at 11:25
Personally, I would say that $ and $ are preferable to $, but since they are (usually) functionally equivalent, many people still prefer the shorter $. See Are ( and ) preferable to dollar signs for math mode? — schtandard, Sep 23 '19 at 12:56

score 14 · Answer 1 · answered Sep 21 '19 at 14:00

A circle with variable line thickness:

\documentclass{article}
\usepackage{amsmath,pict2e}

\makeatletter
\newcommand{\bigcomp}{%
  \DOTSB
  \mathop{\vphantom{\sum}\mathpalette\bigcomp@\relax}%
  \slimits@
}
\newcommand{\bigcomp@}[2]{%
  \begingroup\m@th
  \sbox\z@{$#1\sum$}%
  \setlength{\unitlength}{0.9\dimexpr\ht\z@+\dp\z@}%
  \vcenter{\hbox{%
    \begin{picture}(1,1)
    \bigcomp@linethickness{#1}
    \put(0.5,0.5){\circle{1}}
    \end{picture}%
  }}%
  \endgroup
}
\newcommand{\bigcomp@linethickness}[1]{%
  \linethickness{%
      \ifx#1\displaystyle 2\fontdimen8\textfont\else
      \ifx#1\textstyle 1.65\fontdimen8\textfont\else
      \ifx#1\scriptstyle 1.65\fontdimen8\scriptfont\else
      1.65\fontdimen8\scriptscriptfont\fi\fi\fi 3
  }%
}

\makeatother

\begin{document}

\begin{gather*}
\sum_{i=1}^n \bigcup_{i=1}^n \bigcomp_{i=1}^n f_i\\
\textstyle\sum_{i=1}^n \bigcup_{i=1}^n \bigcomp_{i=1}^n f_i\\
\scriptstyle\sum_{i=1}^n \bigcup_{i=1}^n \bigcomp_{i=1}^n f_i\\
\scriptscriptstyle\sum_{i=1}^n \bigcup_{i=1}^n \bigcomp_{i=1}^n f_i
\end{gather*}

\end{document}

score 6 · Answer 2 · answered Sep 21 '19 at 15:11

Another possible solution, with the \bigovoid symbol from mathabx and \stackinset from stackengine to insert a smaller \bigovoid inside a larger one:

\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
\usepackage{stackengine}

\DeclareFontFamily{U}{mathx}{\hyphenchar\font45}
\DeclareFontShape{U}{mathx}{m}{n}{%
<-6> mathx5
<6-7> mathx6
<7-8> mathx7
<8-9> mathx8
<9-10> mathx9
<10-12> mathx10
<12-> mathx12
}{}

\DeclareSymbolFont{mathx}{U}{mathx}{m}{n}
\DeclareFontSubstitution{U}{mathx}{m}{n}

\DeclareMathSymbol{\bigovoid}{\mathop}{mathx}{"EC}

\newcommand{\BigO}{\mathop{\stackinset{c}{}{c}{}{ \scalebox{1.1}{$\bigovoid$}}{ \scalebox{1.15}{$\bigovoid$}}}}

\newcommand{\bigO}{\mathop{\stackinset{c}{-2pt}{c}{}{ \scalebox{0.8}{$\bigovoid$}}{\scalebox{0.85}{$\bigovoid$}}}}
\usepackage{xcolor}

    \begin{document}

\[ \BigO_{k=0}^{n}f_k \qquad \bigoplus_{k=0}^{n}V_k\]

$ \bigO_{k=0}^{n}f_k \qquad \bigoplus_{k=0}^{n}V_k$

but looking better - comparable in size and boldness to something like $\displaystyle\bigcap$ in $\displaystyle\bigcap_{k=0}^n A_k$ or to $\displaystyle\bigoplus$.

\end{document}

Symbol for function composition like a big sum

2 Answers2