Weird spacing in aligned environment
I'd use an array
environment, which is highly customizable.
\documentclass{article}
\usepackage{array} % for "\newcolumntype" directive
\newcolumntype{C}{>{{}}c<{{}}}
\newcommand\mydots{\multicolumn{1}{l}{\cdots}}
\begin{document}
\[
\setlength\arraycolsep{0pt}
\begin{array}{l*{6}{Cr}}
h_t &=&ca_t&+&2c^2a_{t+1}&+&3c^3a_{t+2}&+&\mydots \\
h_{t+1} &=& & &ca_{t+1} &+&2c^2a_{t+2}&+&3c^3a_{t+3}&+&\mydots \\
h_{t+2} &=& & & & & ca_{t+2}&+&2c^2a_{t+3}&+&3c^3a_{t+4}&+&\mydots
\end{array}
\]
or, if lining up the ``$c$'' coefficients matters too,
\[
\setlength\arraycolsep{0pt}
\begin{array}{l*{6}{Cr}}
h_t &=&c\,a_t&+&2c^2a_{t+1}&+&3c^3a_{t+2}&+&\mydots \\
h_{t+1} &=& & &c^{\phantom{1}}a_{t+1} &+&2c^2a_{t+2}&+&3c^3a_{t+3}&+&\mydots \\
h_{t+2} &=& & & & & c^{\phantom{1}}a_{t+2}&+&2c^2a_{t+3}&+&3c^3a_{t+4}&+&\mydots
\end{array}
\]
\end{document}
Is this what you want?
You have to remember that n alignment points require 2 n – 1 &
. Also, using alignat*
gives you full control on the spacing of the alignment columns.
Unrelated: don't use the TeX construct $$ ... $$
, use the LaTeX construct \[ ... \]
(unnecessary here – use the starred version of the amsmath
environments):
\documentclass[11pt]{article}
\usepackage{amsmath}
\begin{document}
\begin{alignat*}{3}
h_t &= ca_t &{}+2c^2 & a_{t+1} & {}+ 3c^3&a_{t+2}+\dotsb \\
h_{t+1} &= & c \,& a_{t+1} &{} + 2c^2&a_{t+2} + 3c^3a_{t+3}+\dotsb \\
h_{t+2} &= & & & c&a_{t+2} + 2c^2a_{t+3} + 3c^3a_{t+4}+\dotsb
\end{alignat*}
\end{document}
A variant of Mico's answer, with more alignment points, but with easier input, taking advantage of the repetitive structure.
\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\begin{document}
\[
\setlength{\arraycolsep}{0pt}
\newcommand{\row}[1]{%
&
c^{\hphantom{1}} &
a_{t\ifnum#1=0 \else+#1\fi} &
+ &
2 &
c^2 &
a_{t+\number\numexpr#1+1} &
+ &
3 &
c^3 &
a_{t+\number\numexpr#1+2} &
+ &
\multicolumn{3}{l}{\dotsb}
}
\begin{array}{
l % the left hand sides
>{{}}c<{{}} % the equals sign
*{5}{
l % numeric coefficient
l % power of c
c % 'a' term
>{{}}c<{{}} % plus
}
lll % final dots
}
h_t &=& \row{0} \\[\jot]
h_{t+1} &=& &&&& \row{1} \\[\jot]
h_{t+2} &=& &&&&&&&& \row{2}
\end{array}
\]
\end{document}