Help:TeX Examples

Quadratic Polynomial

ax² + bx + c = 0

<math>ax^2 + bx + c = 0</math>

Quadratic Polynomial (Force PNG Rendering)

<math>ax^2 + bx + c = 0\,\!</math>

Quadratic Formula

<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

Tall Parentheses and Fractions

<math>2 = \left(\frac{\left(3-x\right) \times 2}{3-x} \right)</math>

 <math>S_{new} = S_{old} - \frac{ \left( 5-T \right) ^2} {2}</math>
 

Integrals

<math>\int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy</math>

Summation

<math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
 {3^m\left(m\,3^n+n\,3^m\right)}</math>

Differential Equation

<math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math>

Complex numbers

<math>|\bar{z}| = |z|,
 |(\bar{z})^n| = |z|^n,
 \arg(z^n) = n \arg(z)</math>

Limits

<math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math>

Integral Equation

<math>\phi_n(\kappa) =
 \frac{1}{4\pi^2\kappa^2} \int_0^\infty
 \frac{\sin(\kappa R)}{\kappa R}
 \frac{\partial}{\partial R}
 \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR</math>

Example

<math>\phi_n(\kappa) = 
 0.033C_n^2\kappa^{-11/3},\quad
 \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>

Continuation and cases

<math>
 f(x) =
 \begin{cases}
 1 & -1 \le x < 0 \\
 \frac{1}{2} & x = 0 \\
 1 - x^2 & \mbox{otherwise}
 \end{cases}
 </math>

Prefixed subscript

 <math>{}_pF_q(a_1,...,a_p;c_1,...,c_q;z)
 = \sum_{n=0}^\infty
 \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}
 \frac{z^n}{n!}</math>