Aligning long Equations

Question

How could I align the expression [F_{1}(M)\cdot L_{M+1}]_{ij} with the rest of the equations? This is the code I am using:

\begin{align*}
[F_{1}(M)\cdot L_{M+1}]_{ij} \\
&=\sum_{s=1}^{\infty}\prob(\gamma(M+1)<\gamma(0),\phi(\gamma(M+1))=s|X(0)=1,\phi(0)=i)\cdot\\
&\prob(\gamma(M+2)<\gamma(0),\phi(\gamma(M+2))=j|X(0)=M+1,\phi(0)=s)\\
&=\sum_{s=1}^{\infty}\prob(\gamma(M+2)<\gamma(0),\phi(\gamma(M+1))=s,\phi(\gamma(M+2))=j|X(0)=1,\phi(0)=i)\\
&= \prob(\gamma(M+2)<\gamma(0),\phi(\gamma(M+2))=j|X(0)=1,\phi(0)=i) = [F_{1}(M+1)]_{ij}
\end{align*}

The output is like in the attached image.

Answer 1

I'd use something like this

Note I changed your conditional |'s to \mid's to give them better spacing. The normal | kinda drowns

Edit: Missed the \cdot, this is exactly why one never ends a displayed line with a relation or a binary, it gets overlooked.

\documentclass[a4paper]{article}
\usepackage{mathtools,amssymb}
\newcommand\prob{\mathbb{P}}
\begin{document}
\begin{align*}
  \MoveEqLeft[3] [F_{1}(M)\cdot L_{M+1}]_{ij} 
  \\
  = {} &\sum_{s=1}^{\infty}\prob(\gamma(M+1)<\gamma(0),\phi(\gamma(M+1))=s\mid X(0)=1,\phi(0)=i)
  \\
& \cdot  \prob(\gamma(M+2)<\gamma(0),\phi(\gamma(M+2))=j\mid X(0)=M+1,\phi(0)=s)
  \\
  = {} &\sum_{s=1}^{\infty}\prob(\gamma(M+2)<\gamma(0),\phi(\gamma(M+1))=s,\phi(\gamma(M+2))=j \mid X(0)=1,\phi(0)=i)
  \\
  = {} & \prob(\gamma(M+2)<\gamma(0),\phi(\gamma(M+2))=j\mid X(0)=1,\phi(0)=i) = [F_{1}(M+1)]_{ij}
\end{align*}
\end{document}

Answer 2

Here's my suggestion.

Observe that I've replaced all four instances of | with \bigm\vert and manually increased the sizes of the opening and closing parentheses in each line. I'd also place the final term, i.e., [F_{1}(M+1)]^{}_{ij}, on a new row.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb}
\DeclareMathOperator{\prob}{\mathbb{P}}
\begin{document}
\begin{align}
&[F_{1}(M)\cdot L_{M+1}]^{}{ij} \
&= \sum{s=1}^{\infty} \prob\bigl( \gamma(M+1)<\gamma(0),\phi(\gamma(M+1))=s
   \bigm\vert X(0)=1,\phi(0)=i\bigr)\
& \qquad\times \prob\bigl( \gamma(M+2)<\gamma(0),\phi(\gamma(M+2))=j
   \bigm\vert X(0)=M+1,\phi(0)=s \bigr) \
&= \sum_{s=1}^{\infty} \prob\bigl(  \gamma(M+2)<\gamma(0),
   \phi(\gamma(M+1))=s, \phi(\gamma(M+2))=j
   \bigm\vert X(0)=1,\phi(0)=i \bigr) \
&= \prob\bigl( \gamma(M+2)<\gamma(0),\phi(\gamma(M+2))=j 
   \bigm\vert X(0)=1,\phi(0)=i \bigr) \[\jot]
&= [F_{1}(M+1)]^{}_{ij}
\end{align}
\end{document}

Answer 3

My advice is as follows. It's improved from @Mico 's solution:

1. add the indentation by \hptantom of the first line of the equations;
2. add the indentation by \hptantom of the third line of the equations;
3. use \left and \right instead of \bigl and \bigr before parenthesis;
4. use \mid instead of \bigm\vert;
5. delete [\jot] codes of the sixth line of the equations;
6. add the dot . at the end of the last line of equations.

Welcome others to improve the current solution furthermore.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb}
\DeclareMathOperator{\prob}{\mathbb{P}}
\begin{document}
\begin{align}
&\hphantom{=~}[F_{1}(M)\cdot L_{M+1}]^{}{ij} \
&= \sum{s=1}^{\infty} \prob\left(\gamma(M+1)<\gamma(0),\phi(\gamma(M+1))=s
   \mid X(0)=1,\phi(0)=i\right)\
&\hphantom{=\sum_{s=1}^{\infty}}\times \prob\left(\gamma(M+2)<\gamma(0),\phi(\gamma(M+2))=j
   \mid X(0)=M+1,\phi(0)=s \right) \
&= \sum_{s=1}^{\infty} \prob\left(\gamma(M+2)<\gamma(0),
   \phi(\gamma(M+1))=s, \phi(\gamma(M+2))=j
   \mid X(0)=1,\phi(0)=i \right) \
&= \prob\left(\gamma(M+2)<\gamma(0),\phi(\gamma(M+2))=j 
   \mid X(0)=1,\phi(0)=i \right) \
&= [F_{1}(M+1)]^{}_{ij}.
\end{align}
\end{document}