How to deal with long formula?

Question

How to show a formula too long to fit in a line?

For example: $$ P(Y-X=m | Y > X) = \sum_{k} P(Y-X=m, X=k | Y > X) = \sum_{k} P(Y-X=m | X=k, Y > X) P(X=k | Y > X) = \sum_{k} P(Y-k=m | Y > k) P(X=k | Y > X).$$

Thanks!

Answer 1

Use double dollars and the \begin{align*} environment (within TeX-mode) to solve the problem.

$$\begin{align*} P(Y-X=m | Y > X) &= \sum_{k} P(Y-X=m, X=k | Y > X) \\ &= \sum_{k} P(Y-X=m | X=k, Y > X) P(X=k | Y > X) \\ &= \sum_{k} P(Y-k=m | Y > k) P(X=k | Y > X).\end{align*}$$

$$\begin{align*}
P(Y-X=m | Y > X) &= \sum_{k} P(Y-X=m, X=k | Y > X) \ &= \sum_{k} P(Y-X=m | X=k, Y > X) P(X=k | Y > X) \ &= \sum_{k} P(Y-k=m | Y > k) P(X=k | Y > X).\end{align*}$$

Answer 2

Alternatively, since MathJax supports the amsmath extensions, the split environment is also supported:

$$\begin{split}P(Y-X=m | Y > X) &= \sum_{k} P(Y-X=m, X=k | Y > X) \\ &= \sum_{k} P(Y-X=m | X=k, Y > X) P(X=k | Y > X) \\ &= \sum_{k} P(Y-k=m | Y > k) P(X=k | Y > X).\end{split}$$

which is generated by

$$\begin{split} P(Y-X=m | Y > X) &= \sum_{k} P(Y-X=m, X=k | Y > X) \\ &= \sum_{k} P(Y-X=m | X=k, Y > X) P(X=k | Y > X) \\ &= \sum_{k} P(Y-k=m | Y > k) P(X=k | Y > X).\end{split}$$

Answer 3

As the last mathematician in the world still using Plain TeX, I'd do it with eqalign.

$$\eqalign{P(Y-X=m\mid Y\gt X)&=\sum_kP(Y-X=m,X=k\mid Y\gt X)\cr&=\sum_kP(Y-X=m\mid X=k,Y\gt X)\,P(X=k\mid Y>X)\cr&=\sum_kP(Y-k=m\mid Y\gt k)\,P(X=k\mid Y\gt X)\cr}$$

\eqalign{
  P(Y-X=m\mid Y\gt X)
    &=\sum_kP(Y-X=m,X=k\mid Y\gt X)\cr
    &=\sum_kP(Y-X=m\mid X=k,Y\gt X)\,P(X=k\mid Y>X)\cr
    &=\sum_kP(Y-k=m\mid Y\gt k)\,P(X=k\mid Y\gt X)\cr
}