# How do I modify the size of S the summation operand?

I bet this fancy summation operand S is in fact $\mathcal{S}$, am I right?

But how do I modify the size of this thingy? \bigg or \left\right doesn't seem to work...

And something like this: $\mathcal{S}^b_a\frac k2$ looks well... not very nice:

Not sure if you really want the calligraphic S to be sized as the summation symbol, taking limits above and below in display style, but here it is:

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

\makeatletter
\newcommand{\fancysum}{%
\mathop{%
\vphantom{\sum}%
\mathpalette\fancy@sum\relax
}\slimits@
}
\newcommand{\fancy@sum}[2]{%
\sbox\z@{$#1\sum$}%
\dimen@=\ht\z@
\vcenter{\hbox{%
\resizebox{!}{\ifx#1\displaystyle.9\fi\dimen@}{%
$\m@th\mathcal{S}$%
}%
}}%
}
\makeatother

\begin{document}
$\sum_{k=a}^{b} \fancysum_{k=a}^{b}\frac{k}{2} \textstyle\sum\fancysum \scriptstyle\sum\fancysum$
\end{document}


The \textstyle and \scriptstyle declarations are just by way of example, in order to show that the symbol scales properly.

I added a 0.9 factor in displaystyle or the overshoot would become too prominent.

Here is an option using \mathchoice, where you can adjust the parameters to suit your needs:

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

\DeclareMathOperator*{\fancysum}{%
\mathchoice% http://tex.stackexchange.com/q/148740/5764
{\raisebox{-.325\height}{\scalebox{2.2}{$\mathcal{S}$}}}% \displaystyle
{\raisebox{-.25\height}{\scalebox{1.5}{$\mathcal{S}$}}}% \textstyle
{\raisebox{-.2\height}{\scalebox{0.95}{$\mathcal{S}$}}}% \scriptstyle
{\raisebox{-.25\height}{\scalebox{0.75}{$\mathcal{S}$}}}}% \scriptscriptstyle

\begin{document}

$\renewcommand{\arraystretch}{3} \begin{array}{c} \displaystyle \sum_2^1 \frac{12}{2} \quad \fancysum_2^1 \frac{12}{2} \\ \textstyle \sum_2^1 \frac{12}{2} \quad \fancysum_2^1 \frac{12}{2} \\ \scriptstyle \sum_2^1 \frac{12}{2} \quad \fancysum_2^1 \frac{12}{2} \\ \scriptscriptstyle \sum_2^1 \frac{12}{2} \quad \fancysum_2^1 \frac{12}{2} \end{array}$

\end{document}


Based on my answer at How are big operators defined?. I provide two versions, depending on whether you want it large in \displaystyle or to keep it text-size in that style.

It is made to occupy the same vertical size as the summation operator, and should behave as such for the purpose of its indices.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\DeclareMathOperator*{\foo}{\scalerel*{\mathcal{S}}{\sum}}
\DeclareMathOperator*{\barr}{\scalerel*{\mathcal{S}}{\textstyle\sum}}
\usepackage{scalerel}

\begin{document}
$\foo_{i=3}^{6}(f^2(i))$

This is inline: $$\foo_{i=3}^{6}(f^2(i))$$

$\barr_{i=3}^{6}(f^2(i))$

This is inline: $$\barr_{i=3}^{6}(f^2(i))$$

$\foo_a^b f = g\rvert_a^b = \sum_{k=a}^{b-1} f(k)$
\end{document}