Typing a specific type of matrix

Question

I am looking to accomplish the following:

So far I have the following code but it's just not quite right

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\left(
 \begin{matrix}
  \nu+\tfrac{1}{2}\\
  2\nu+1\\
 \end{matrix}
\right\rvert\,2iz
\end{document}

Which compiles as

Answer 1

(updated the answer to address @yarchik's comment)

Here are two solutions. The first uses \mleft(, \middle|, and \mright), where \mleft and \mright are macros provided by the mleftright package. The second uses \Bigl(, \Bigm\vert, and \Bigr). Both solutions avoid creating an excessive amount of space to the left of the opening parenthesis -- a problem that arises when using \left( and \right).

\documentclass{article}
\usepackage{mleftright} % for \mleft and \mright macros
\begin{document}

\[
  {}_1F_1 
  \mleft( 
  \begin{array}{@{}c@{}}
    \nu+\frac{1}{2} \\ 2\nu+1 
  \end{array} 
  \,\middle|\,
  2iz \mright)
  \qquad
  {}_1F_1 
  \Bigl( 
  \begin{array}{@{}c@{}}
    \nu+0.5 \\ 2\nu+1 
  \end{array} 
  \Bigm\vert
  2iz \Bigr)
\]

\end{document}

Answer 2

This is a perfect place to use amsmath's \genfrac command.

\documentclass{article}
\usepackage{amsmath}
\newcommand\hypergeom[3]{{}_1F_1\left(\genfrac{}{}{0pt}{}{#1}{#2}\,\middle\vert\,#3\right)}

\begin{document}
\[ \hypergeom{\nu+\frac12}{2\nu+1}{2iz} \]
\end{document}

Explanation

In the definition above, we first have \left( ... \,\middle\vert\, ... \right); this generates automatically resized ( | ) that shows up. The \, is used to add some spacing, the \middle applied to \vert makes the vertical line grow in the same way as the parentheses to accommodate the arguments.

The heavy lifting is done by the \genfrac command, which amsmath uses to create things like \tfrac and \binom. Here we just want to stack two terms one over another, and so we basically ignore the first four arguments. For more bout the \genfrac command, see the amsmath documentation.

An advantage of using \genfrac is that it follows automatically scaling when you use the command in in-line math versus in display math. See the image below:

The top line uses the \hypergeom macro defined above; the bottom line uses a matrix based incantation. For things like the hypergeometric function, the down-sized expression (similar to how in-line fractions are smaller compared to display ones) is, in my opinion, more pleasing.

Answer 3

There are several ways. You can place the | character inside mathrel for proper spacing. Then adjust its size with \Big or \bigg if you want it bigger. Manually sizing the delimiters ( and ) will generally give you better results than using \left( and \right).

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
\biggl(
 \begin{matrix}
  \nu+\tfrac{1}{2}\\
  2\nu+1\\
 \end{matrix}
\mathrel{\Big|} 2iz\biggr)
\]
\end{document}