issues with fractions

Question

I have:

\usepackage{nicefrac }
\begin{align*}
&= \frac{2}{\sqrt{2y+1}\sqrt{2 \pi}}  \exp \left( -y-\nicefrac{1}{2} \right)  &&\forall y \in  [-\frac{1}{2} , \infty) \\
&= \frac{2}{\sqrt{2y+1}\sqrt{2 \pi}}  \exp \left( -y-\frac{1}{2} \right)  &&\forall y \in  [-\nicefrac{1}{2} , \infty) 
\end{align*}

Both of these seem somewhat unsatisfactory. Could anyone help me get the best display for the 1/2 after the \exp ( and also after the \in [

Answer 1

Fractions

I'd just use the normal \frac or \tfrac. For display style maths they still look the best. I would use \nicefrac (or similar) only (if at all) in text maths.

Code

\documentclass{article}
\usepackage{amsmath}
\def\frstfrac{\frac{2}{\sqrt{2y+1}\sqrt{2 \pi}}} % just a shortcut
\begin{document}
\begin{align*}
  &= \frstfrac       \exp \left(            -y - \frac{1}{2}\right)  && \forall y \in  \left[- \frac{1}{2}, \infty\right) \\
  &= \frstfrac \cdot  e^{                   -y - \frac{1}{2}}        && \forall y \in  \left[-\tfrac{1}{2}, \infty\right) \\
  &= \frstfrac \cdot  e^{           -  \left(y + \frac{1}{2}\right)} && \forall y \in  \left[-\tfrac{1}{2}, \infty\right) \\
  &= \frstfrac \cdot  e^{\textstyle -\!\left(y + \frac{1}{2}\right)} && \forall y \in  \left[-\tfrac{1}{2}, \infty\right) \\
  &= \frstfrac       \exp \left(            -y - 1/2 \right)         && \forall y \in  \left[-       1/ 2 , \infty\right)
\end{align*}
\end{document}

Output

\smash

Also, consider using \sqrt{\smash[b]{2y+1}}\sqrt{\smash[b]{2 \pi}} in your denominator for better roots.

To quote from the amsmath documentation:

With the amsmath package \smash has optional arguments t and b, because occasionally it is advantageous to be able to “smash” only the top or only the bottom of something while retaining the natural depth or height.

Compare:

Code

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
  \frac{2}{\sqrt{\smash[b]{2y+1}}\sqrt{\smash[b]{2 \pi}}} = \frac{2}{\sqrt{2y+1}\sqrt{2 \pi}}
\end{equation*}
\end{document}

Output

The top bar of the root is aligned different and even the lower point is not on equal heights.

LaTeX Companion

The LaTeX Companion has a very elaborated text about \smash and its uses. The first two examples (licensed under the LPPL) are shown here. Take a close look at the root's lower end and the top bar.

Code

\documentclass{article}
\usepackage{amsmath}
\begin{document}

$ \sqrt{x} + \sqrt{y}            + \sqrt{z} $ \par
$ \sqrt{x} + \sqrt{\mathstrut y} + \sqrt{z} $ \par
$ \sqrt{x} + \sqrt{\smash{y}}    + \sqrt{z} $ \par
$ \sqrt{x} + \sqrt{\smash[b]{y}} + \sqrt{z} $

\[
   \sqrt{ \frac{a+b}{         x_j   } } \quad
   \sqrt{ \frac{a+b}{  \smash{x_j  }} } \quad
   \sqrt{ \frac{a+b}{{}\smash{x_j  }} } \quad
   \sqrt{ \frac{a+b}{  \smash{x_j+b}} }
\]
\end{document}

Output