Latex formula number, inline formula, formula space, long formula wrap, inline hyphen symbol

first, the formula number\begin{equation}
X (k) =\sum_{n=0}^{n-1} x (n) e^{-j \frac{2 \pi}{n} k n}=\sum_{n=0}^{n-1} x (n) w_n^{kn},\quad k=0,1,..., N-1.
\end{equation}

Next paragraph
(1)Add Begin{equation} and End{equation}, the formula will be automatically numbered; (2)The formula will be empty one line after another paragraph, or the next paragraph will not automatically indent the beginning.
two, in-line formulaIn-line formula: $ formula $ another line formula: $$ formula $$
three, the formula inside the space

Two x Quad spaces	A \qquad b		Width of two M
Quad spaces	A \quad b		The width of a m
Large space	A\ b		1/3m width
Medium space	A\;b		2/7m width
Small spaces	A\,b		1/6m width
No spaces	Ab
Close	A\!b		Indent 1/6m Width

three, long formula line
Using split: \begin{equation}
\begin{split}
F = \{f_{x} \in f_{c} &: (| s| > | c|) \\
&\quad \cap (\text{minpixels} < | s| < \text{maxpixels}) \ \
&\quad \cap (| s_{\text{conected}}| > | s| -\epsilon) \}
\end{split}
\end{equation}

where \ \ represents the aligned position of the newline,&.

four, inline plus symbolIf written as $\sum_{k=0}^{n-1}$, the hyphen in the line will be written in the above and the following parameters as a corner label, should be written as $\sum\limits_{k=0}^{n-1}$, when the inline symbol does not change.

Formula number advanced:

If you use the eqnarray environment , you can only display the numbers behind the above or the following equation, such as:
\begin{eqnarray}
a+b = 1 \ \
C+d = 2
The \end{eqnarray} number is displayed after the second equation.

Use the following statement to make the numbering appear in the middle of two equations:
\begin{equation}
\BEGIN{ARRAY}{L}
A+b=1 \ \
c+d=2
\end{array}
\end{equation}

Sometimes it is crowded between the following equations to avoid this situation by adding \displaystyle to each equation, such as:
\begin{equation}
\BEGIN{ARRAY}{L}
\displaystyle a+b=1 \ \
\displaystyle c+d=2
\end{array}
\end{equation}

The split environment can also be used to write numbers in the middle, such as:
\begin{equation}
\begin{split}
a+b=1\\
c+d=2
\end{split}
\end{equation}