tag moves equation position

Question

although there seems to be enough space between the second equation and the tag, the equation is not fully centered. is there a way to suppress this spacing behaviour so that the equation stays centered? i don't intend to align different equations but to center equations of different length when using a tag, provided that there would not be any overlapping.

\documentclass{scrartcl}

\usepackage{amsmath}
\usepackage{lipsum}

\begin{document}

\lipsum[1]

\begin{equation*}
h(z)=f(z)-\sum_{j=1}^m a_j(z-z_0)^{-j}
\end{equation*}

\begin{equation*}
h(z)=f(z)-\sum_{j=1}^m a_j(z-z_0)^{-j},\tag{$z\in D\setminus\{ z_0 \}$}
\end{equation*}

\lipsum[1]

\end{document}

Answer 1

Here are three other solutions:

\documentclass{scrartcl}
\usepackage{mathtools}
\newtagform{mytag}{\llap\bgroup(}{)\egroup}

\begin{document}

\usetagform{mytag}
\begin{align*} 
h(z)&=f(z)-\sum_{j=1}^m a_j(z-z_0)^{-j}\\
h(z)&=f(z)-\sum_{j=1}^m a_j(z-z_0)^{-j},\tag{{$z\in D\setminus\{ z_0 \}$}}
\end{align*}
\usetagform{default}

\begin{align*}
   h(z)&=f(z)-∑_{j=1}^m a_j(z-z₀)^{-j}\\
    h(z) & =f(z)-∑_{j=1}^m a_j(z-z₀)^{-j}, \mathrlap{\qquad z ∈ D∖\{ z₀ \}}
\end{align*}

\begin{flalign*}
  & & h(z)&=f(z)-∑_{j=1}^m a_j(z-z₀)^{-j}\\
  & & h(z)&=f(z)-∑_{j=1}^m a_j(z-z₀)^{-j}, & & \mathllap{z ∈ D∖\{ z₀ \}}
\end{flalign*}

\end{document} 

Answer 2

Using align environment can help,

\documentclass{scrartcl}

\usepackage{amsmath}
\usepackage{lipsum}

\begin{document}

\lipsum[1]

\begin{align*}
h(z)&=f(z)-\sum_{j=1}^m a_j(z-z_0)^{-j}\\
h(z)&=f(z)-\sum_{j=1}^m a_j(z-z_0)^{-j},\tag{$z\in D\setminus\{ z_0 \}$}
\end{align*}

\lipsum[1]

\end{document}