Consider a definition of iterative function composition in a mathematical document:
\begin{align*}
\bigcirc_{i = l}^{u}\ f_i &= \mathrm{id}_A \\
\bigcirc_{i = l}^{u}\ f_i &= f_l \circ (\bigcirc_{i = l + 1}^{u}\ f_i)
\end{align*}
What i don't like is the placement of i = l and u, because it should be directly below and above the big circle in displaymath. Now look at this example:
\begin{align*}
\bigodot_{i = l}^{u} f_i &= \mathrm{id}_A \\
\bigodot_{i = l}^{u} f_i &= f_l \circ (\bigodot_{i = l + 1}^{u} f_i)
\end{align*}
That way the placement is as I wish, but now the big cirle has a little spot within in. I would like to achieve the placement of the second example, but with the symbol of the first example. Is there a way to do that?
By the way, here's an MWE:
\documentclass[a4paper,10pt]{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\bigcirc_{i = l}^{u}\ f_i &= \mathrm{id}_A && \text{if $l > u$}\\
\bigcirc_{i = l}^{u}\ f_i &= f_l \circ (\bigcirc_{i = l + 1}^{u}\ f_i) && \text{otherwise}
\end{align*}
\begin{align*}
\bigodot_{i = l}^{u} f_i &= \mathrm{id}_A && \text{if $l > u$}\\
\bigodot_{i = l}^{u} f_i &= f_l \circ (\bigodot_{i = l + 1}^{u} f_i) && \text{otherwise}
\end{align*}
\end{document}
\mathop{\bigcirc}\limits_{i = l}^{u}
or else\DeclareMathOperator*\bigcircop{\bigcirc}
and\bigcircop_{i = l}^{u}