How to make x and y, which stand after the vertical line, have the same size as the small \psi and x, which stand in \partial

Question

\begin{equation*}
\psi(\omega) = \left.{\psi}\right|_{\omega=0} +
 \omega \cdot 
 \underbrace {\left.\dfrac{d\psi}{d\omega}\right|_{\omega=0} }_{\left.\frac{\partial \psi}{\partial x}\right|_{\substack{{x =0} \\ {y=0}}}} \,+ \,\dfrac{\omega^2}{2} \,\cdot\, \underbrace {\left.\dfrac{d^2\psi}{d\omega \, d\omega}\right|_{\substack{\omega=0}}}_{\left.\frac{\partial \psi^2}{\partial x \partial x}\right|_{\substack{x=0 \\ y=0 }}} + \ldots +
   \dfrac{\omega^p}{p!} \cdot \dfrac{d^p\psi}{d\omega \cdot \ldots \cdot d\omega}
\end{equation*}

Answer 1

Rather than miniaturize the arguments of the \substack directives, I would increase the size of the associated fraction expressions, by using \tfrac instead of \frac.

\documentclass{article}
\usepackage{amsmath,xcolor}
\begin{document}
\textcolor{red}{Before}
\begin{equation}
\psi(\omega) = \left.{\psi}\right|{\omega=0} +
 \omega \cdot 
 \underbrace {\left.\dfrac{d\psi}{d\omega}\right|{\omega=0} }{\left.\frac{\partial \psi}{\partial x}\right|{\substack{{x =0} \ {y=0}}}} ,+ ,\dfrac{\omega^2}{2} ,\cdot, \underbrace {\left.\dfrac{d^2\psi}{d\omega , d\omega}\right|{\substack{\omega=0}}}{\left.\frac{\partial \psi^2}{\partial x \partial x}\right|_{\substack{x=0 \ y=0 }}} + \ldots +
   \dfrac{\omega^p}{p!} \cdot \dfrac{d^p\psi}{d\omega \cdot \ldots \cdot d\omega}
\end{equation}
\medskip
\textcolor{red}{After}
\begin{equation*}
\psi(\omega) = \psi\bigr|{\omega=0} +
 \omega \cdot 
  {\underbrace {\frac{d\psi}{d\omega}\biggr|{\omega=0} }%
 {\tfrac{\partial\psi}{\partial x}\Bigr|{\substack{x =0\y=0 }}}}



\frac{\omega^2}{2} \cdot 
  {\underbrace{\frac{d^2\psi}{d\omega,d\omega}\biggr|{\omega=0}}%
 _{\tfrac{\partial^2\psi}{\partial x,\partial x}\Bigr|{\substack{x=0 \ y=0 }}}}

\dots +

\frac{\omega^p}{p!} \cdot 
\frac{d^p\psi}{d\omega \ldots d\omega}
\end{equation*}
\end{document}

Answer 2

LaTeX use 4 math styles: \displaystyle, \textstyle, \scriptstyle and \scriptscriptstyle. The smallest is \scriptscriptstyle.

\substack, like the subarray environment use \scriptstyle. As a workaround, force \scriptscriptstyle inside:

\substack{\scriptscriptstyle x =0 \\ \scriptscriptstyle y=0}