User:Ahadland123

Quadratic formula

 * $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Tall Parentheses and Fractions
\frac{\left(3-x\right) \times 2}{3-x} \right)$$
 * $$2 = \left(

\frac{ \left( 5-T \right) ^2} {2}$$
 * $$S_{new} = S_{old} +

Integrals

 * $$\int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy$$


 * $$\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}$$

Differential equation

 * $$u'' + p(x)u' + q(x)u=f(x),\quad x>a$$

Complex numbers

 * $$|bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)$$

Limits
$$\lim_{z\rightarrow z_0} f(z)=f(z_0)$$

Integral equation
= \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$$
 * $$\phi_n(\kappa)

Example
$$
 * $$\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{1_0}

Continuation and cases
$$f(x) = \begin{cases}1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 = x^2 & 0 < x \le 1\end{cases}$$

Prefixed subscript
$${}_pF_q(a_1,...,a_p;c_1,...,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}\frac{z^n}{n!}$$