Dots (LaTeX2e unofficial reference manual (November 2018))

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#### 16.2.6 Dots, horizontal or vertical

Ellipses are the three dots (usually three) indicating that a pattern continues.

    \begin{array}{cccc}
      a_{0,0}    &a_{0,1}   &a_{0,2} &\ldots \\
      a_{1,0}    &\ddots                     \\
      \vdots
    \end{array}

LaTeX provides these.

`\cdots`

  Horizontal ellipsis with the dots raised to the center of the line, as in ⋯. Used as: `\( a_0\cdot a_1\cdots a_{n-1} \)`.

`\ddots`

  Diagonal ellipsis, ⋱. See the above array example for a usage.

`\ldots`

  Ellipsis on the baseline, …. Used as: `\( x_0,\ldots x_{n-1} \)`. Another example is the above array example. A synonym is `\mathellipsis`. A synonym from the `amsmath` package is `\hdots`.

  You can also use this command outside of mathematical text, as in `The gears, brakes, \ldots{} are all broken`. (In a paragraph mode or LR mode a synonym for `\ldots` is `\dots`.)

`\vdots`

  Vertical ellipsis, ⋮. See the above array example for a usage.

The `amsmath` package has the command `\dots` to semantically mark up ellipses. This example produces two different-looking outputs for the first two uses of the `\dots` command.

    \usepackage{amsmath}  % in preamble
      ...
    Suppose that \( p_0, p_1, \dots, p_{n-1} \) lists all of the primes.
    Observe that \( p_0\cdot p_1 \dots \cdot p_{n-1} +1 \) is not a
      multiple of any \( p_i \).
    Conclusion: there are infinitely many primes \( p_0, p_1, \dotsc \).

In the first line LaTeX looks to the comma following `\dots` to determine that it should output an ellipsis on the baseline. The second line has a `\cdot` following `\dots` so LaTeX outputs an ellipsis that is on the math axis, vertically centered. However, the third usage has no follow-on character so you have to tell LaTeX what to do. You can use one of the commands: `\dotsc` if you need the ellipsis appropriate for a comma following, `\dotsb` if you need the ellipses that fits when the dots are followed by a binary operator or relation symbol, `\dotsi` for dots with integrals, or `\dotso` for others.

Unofficial LaTeX2e reference manual