Examples of Mathematical Equations Using LaTeX

First Example

Wiki markup:

%\[
\int_{-\infty}^\infty e^{-\alpha x^2} dx = \sqrt{\frac{\pi}{\alpha}}
\]%

Result:

%\[ \int_{-\infty}^\infty e^{-\alpha x^2} dx = \sqrt{\frac{\pi}{\alpha}} \]%

Second Example

Wiki markup:

%BEGINLATEX{color="Maroon" bgcolor="Yellow"}%
\begin{multline*}
\cal A, B, C, D, E, F, G, H, I, J, K, L, M, \\
\cal N, O, P, Q, R, S, T, U, V, W, X, Y, Z
\end{multline*}
%ENDLATEX%

Result:

%BEGINLATEX{color="Maroon" bgcolor="Yellow"}% \begin{multline*} \cal A, B, C, D, E, F, G, H, I, J, K, L, M, \\cal N, O, P, Q, R, S, T, U, V, W, X, Y, Z \end{multline*} %ENDLATEX%

Third Example

Wiki markup:

%\[ \sum_{i_1, i_2, \ldots, i_n} \pi * i + \sigma \]%

Result:

%\[ \sum_{i_1, i_2, \ldots, i_n} \pi * i + \sigma \]%

Fourth Example

Wiki markup:

%BEGINLATEX%
\begin{equation*}
\begin{split}
H_c&=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2}
\sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\
&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
\Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr].
\end{split}
\end{equation*}
%ENDLATEX%

Result:

%BEGINLATEX% \begin{equation*} \begin{split} H_c&=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2} \sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot \Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr]. \end{split} \end{equation*} %ENDLATEX%

Fifth Example

Wiki markup:

%\[ \omega_p = \sqrt { \frac{n_e \, e^2}{\epsilon_0 \, m_e} } \]%

Result:

%\[ \omega_p = \sqrt { \frac{n_e \, e^2}{\epsilon_0 \, m_e} } \]%

Sixth Example

Wiki markup:

%\[
\left|\sum_{i=1}^n a_ib_i\right| \le
\left(\sum_{i=1}^n a_i^2\right)^{1/2}
\left(\sum_{i=1}^n b_i^2\right)^{1/2}
\]%

Result:

%\[ \left|\sum_{i=1}^n a_ib_i\right| \le \left(\sum_{i=1}^n a_i^2\right)^{1/2} \left(\sum_{i=1}^n b_i^2\right)^{1/2} \]%

Seventh Example

Wiki markup:

%BEGINLATEX{label="1"}%
\begin{gather*}
f(x) = \sqrt{1+x}, \quad x \ge -1 \\
f(x) \sim x^2, \quad x\to\infty
\end{gather*}
%ENDLATEX%

Result:

%BEGINLATEX{label="1"}% \begin{gather*} f(x) = \sqrt{1+x}, \quad x \ge -1 \f(x) \sim x^2, \quad x\to\infty \end{gather*} %ENDLATEX%

Eighth Example

Wiki markup:

%BEGINLATEX{label="two"}%
\begin{eqnarray*}
   \textbf{T} &=&
   \begin{pmatrix}
      T_{++} \hfill & T_{+-} \\
      T_{-+} & T_{--} \hfill
   \end{pmatrix}
\\
   & = &
   \begin{pmatrix}
      e^{\beta (J + B)} \hfill & e^{-\beta J} \hfill \\
      e^{-\beta J} \hfill & e^{\beta (J - B)} \hfill
   \end{pmatrix}
\end{eqnarray*}
%ENDLATEX%

Result:

%BEGINLATEX{label="two"}% \begin{eqnarray*} \textbf{T} &=& \begin{pmatrix} T_{++} \hfill & T_{+-} \\ T_{-+} & T_{--} \hfill \end{pmatrix} \ & = & \begin{pmatrix} e^{\beta (J + B)} \hfill & e^{-\beta J} \hfill \\ e^{-\beta J} \hfill & e^{\beta (J - B)} \hfill \end{pmatrix} \end{eqnarray*} %ENDLATEX%

Ninth Example

Wiki markup:

%\[
\boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}
\]%

Result:

%\[ \boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))} \]%

Tenth Example

Wiki markup:

%\[
\Re{z} =\frac{
   n\pi \dfrac{\theta +\psi}{2}
}
{
   \left(\dfrac{\theta +\psi}{2}\right)^2 +
   \left( \dfrac{1}{2} \log \left\lvert\dfrac{B}{A}\right\rvert\right)^2
}
\]%

Result:

%\[ \Re{z} =\frac{ n\pi \dfrac{\theta +\psi}{2} } { \left(\dfrac{\theta +\psi}{2}\right)^2 + \left( \dfrac{1}{2} \log \left\lvert\dfrac{B}{A}\right\rvert\right)^2 } \]%

Eleventh Example

Wiki markup:

Inline math equations, like %$x^y$% and %$x_n = \sqrt{a + b}$%,
are possible.

Result:

Inline math equations, like %$x^y$% and %$x_n = \sqrt{a + b}$%, are possible.

Twelth Example

Wiki markup:

%\[
P_{r-j}=
\begin{cases}
0& \text{if $r-j$ is odd},\\
r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}.
\end{cases}
\]%

Result:

%\[ P_{r-j}= \begin{cases} 0& \text{if $r-j$ is odd},\r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}. \end{cases} \]%

Referencing Equations

See Eq. %REFLATEX{1}% (wiki markup: %REFLATEX{1}%) and Eq. %REFLATEX{two}% (wiki markup: %REFLATEX{two}%).

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