Modify particular symbol after loading a font in XeLaTeX

Question

Here is a MWE

\documentclass[]{article}
\usepackage[no-math]{fontspec}
\setmainfont{Old Standard}[
FakeBold=2,
%SmallCapsFont=PlayfairDisplaySC-Black.otf,
%BoldFont=ModernMTStd-Bold.otf,
%ItalicFont=ModernMT-ExtendedItalic.otf,
%BoldItalicFont=ModernMT-ExtendedItalic.otf,
Ligatures=TeX,]
\usepackage{unicode-math}
\setmathfont{NewCMMath-Book.otf}[FakeBold=2]
\newfontfamily{\bask}{GFS Baskerville}
\let\sum\relax
\DeclareMathOperator*{\sum}{\raisebox{-3.5pt}{\scalebox{2}{{{\bask Σ}}}}}
\title{Test}
\author{Me}
\begin{document}
    \maketitle
    Just testing if the sum operator works.
        \begin{align}
            F(n)
                & = \sum_{d\mid n}f(d)\
            a
                & \geq b\
            f
                & :\mathbb{N}\to\mathbb{N}\
            f\ast g
                & = \sum_{d\mid n}f(d)g(n/d)
        \end{align}
\end{document}

I am trying to modify the summation symbol to look like I took this formula from the answer by ɪdɪət strəʊlə in this post: Old-style/Antique typesetting in LaTeX/TeX

Currently, the output looks like this:

Answer 1

You're almost there, but the change should be done at begin document, because unicode-math redefines there \sum and all other math commands.

There's a better approach, though, so \sum will respect the options to amsmath about limit placement. The symbol will scale according to the current math style and with \vcenter you don't have to guess the amount of lowering.

\documentclass[]{article}
\usepackage{amsmath}
\usepackage[no-math]{fontspec}
\usepackage{unicode-math}
\usepackage{graphicx}
%\setmainfont{Old Standard}[FakeBold=2]
\setmathfont{NewCMMath-Book.otf}[FakeBold=2]
\newfontfamily{\bask}{GFS Baskerville}
\makeatletter
\RenewDocumentCommand{\sum@}{}{\DOTSB\baskervillesum}
\AtBeginDocument{%
  \RenewDocumentCommand{\sum}{}{\mathop{\sum@}\slimits@}%
}
\NewDocumentCommand{\baskervillesum}{}{%
  \mathchoice
   {\makebaskervillesum{2}}% displaystyle
   {\makebaskervillesum{1.5}}% textstyle
   {\makebaskervillesum{1}}% scriptstyle
   {\makebaskervillesum{0.7}}% scriptscriptstyle
}
\NewDocumentCommand{\makebaskervillesum}{m}{%
  \vcenter{\hbox{\scalebox{#1}{\bask Σ}}}%
}
\begin{document}
\begin{align}
  F(n)    & = \sum_{d\mid n}f(d)\
  f\ast g & = \sum_{d\mid n}f(d)g(n/d)
\end{align}
\begin{center}% for testing the other styles
$\sum_{d\mid n}f(d)$
$\scriptstyle\sum_{d\mid n}f(d)$
$\scriptscriptstyle\sum_{d\mid n}f(d)$
\end{center}
\end{document}