Aiuto:Formule matematiche TeX

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${\displaystyle ax^{2}+bx+c=0}$

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

${\displaystyle x_{1,2}={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}$

<math>x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

${\displaystyle {\sqrt {256}}=16}$

<math>\sqrt{256}=16</math>

${\displaystyle {\sqrt[{5}]{32}}=2}$

<math>\sqrt[5]{32}=2</math>

${\displaystyle {\begin{cases}3x-y+8=0\\7-6x+12y=0\\\end{cases}}}$

<math>\begin{cases} 3x-y+8=0\\
7-6x+12y=0\\
\end{cases}</math>

${\displaystyle \log _{a}{b}={\frac {\log _{c}{b}}{\log _{c}{a}}}}$

<math>\log_{a}{b}=\frac{\log_{c}{b}}{\log_{c}{a}}</math>

${\displaystyle 2=\left[{\frac {\left(3-x\right)\times 2}{3-x}}\right]}$

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

${\displaystyle \int _{a}^{x}\int _{a}^{s}f(y)\,dy\,ds=\int _{a}^{x}f(y)(x-y)\,dy}$

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

${\displaystyle \sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {m^{2}\,n}{3^{m}\left(m\,3^{n}+n\,3^{m}\right)}}}$

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

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

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

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

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

${\displaystyle \lim _{z\rightarrow z_{0}}f(z)=f(z_{0})}$

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

Per limiti in due variabili:

${\displaystyle \lim _{(x,y)\to (x_{0},y_{0})}f(x,y)=f(x_{0},y_{0})}$

<math>\lim_{(x,y) \to (x_0 , y_0)} f(x,y)=f(x_0,y_0)</math>

oppure indicato con ${\displaystyle \mathbf {x} =(x,y)}$ e ${\displaystyle \mathbf {x} _{0}=(x_{0},y_{0})}$

${\displaystyle \lim _{\mathbf {x} \to \mathbf {x} _{0}}f(\mathbf {x} )=f(\mathbf {x} _{0})}$

<math>\lim_{\mathbf{x} \to \mathbf{x}_0} f(\mathbf{x})=f(\mathbf{x}_0)</math>

${\displaystyle \phi _{n}(\kappa )={\frac {1}{4\pi ^{2}\kappa ^{2}}}\int _{0}^{\infty }{\frac {\sin(\kappa R)}{\kappa R}}{\frac {\partial }{\partial R}}\left[R^{2}{\frac {\partial D_{n}(R)}{\partial R}}\right]\,dR}$

<math>\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>

${\displaystyle \phi _{n}(\kappa )=0,\!033\,C_{n}^{2}\,\kappa ^{-11/3},\quad {\frac {1}{L_{0}}}\ll \kappa \ll {\frac {1}{l_{0}}}}$

<math>\phi_n(\kappa) = 0,\!033 \, C_n^2 \, \kappa^{-11/3},
  \quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>

${\displaystyle f(x)={\begin{cases}1&-1\leq x<0\\{\frac {1}{2}}&x=0\\x&0<x\leq 1\end{cases}}}$

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

${\displaystyle {}_{p}F_{q}(a_{1},\dots ,a_{p};c_{1},\cdots ,c_{q};z)=\sum _{n=0}^{\infty }{\frac {(a_{1})_{n}\cdots (a_{p})_{n}}{(c_{1})_{n}\cdots (c_{q})_{n}}}{\frac {z^{n}}{n!}}}$

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