It is fairly elementary to align both equations, as well as their variable domains, when defining your own "cases
environment" via an array
:
\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\begin{align*}
T_{\text{in general}}\left(n\right) &= aT\left(\frac{n}{b}\right) + n^{c}, && a\geq 1, b\geq 1, c>0 \\
& && a>b^{c} \\
T_{\text{cases}}\left(n\right) &=
\smash{\left\{\begin{array}{@{}l@{}}
\Theta\left(n^{\log_{b}a}\right) \\[\jot]
\Theta\left(n^{c}\log_{b}n\right) \\[\jot]
\Theta\left(n^{c}\right)
\end{array}\right.} && a=b^{c} \\
& && a<b^{c}
\end{align*}
\end{document}
Some minor alignment adjustments were made (like using additional &
alignment specifiers), as well as \smash
ing the "cases
environment" and adding the [\jot]
line skip. \smash
removed any vertical height from it's argument, while \jot
is a specific 3pt
skip provided by LaTeX.
From a typesetting point of view, note the use of \text{...}
in the subscripts. This macro is offered by amsmath
and allows text to be typeset in the regular way, while still adjusting for the relative size of the font depending on the placement.