User:Ahadland123

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Contents

[edit] Quadratic formula

  • x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

[edit] Tall Parentheses and Fractions

  • 2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)
  • S_{new} = S_{old} + \frac{ \left( 5-T \right) ^2} {2}

[edit] 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)}

[edit] Differential equation

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

[edit] Complex numbers

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

[edit] Limits

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

[edit] Integral equation

  • \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

[edit] Example

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

[edit] 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}

[edit] 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!}