Luokka:Matematiikka

Luokka:Matematiikka

85-;+98.58=${\displaystyle \sum _{n=0}^{\infty }{\frac {x^{n}}{n!}}}$/∞√89!523 ‰(≤783=980.65Y[67∂]ax2 + bx + c = 0 ${\displaystyle ax^{2}+bx+c=0}$${\displaystyle ax^{2}+bx+c=0\,}$ ${\displaystyle x_{1,2}={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}$${\displaystyle 2=\left({\frac {\left(3-x\right)\times 2}{3-x}}\right)}$${\displaystyle S_{new}=S_{old}+{\frac {\left(5-T\right)^{2}}{2}}}$${\displaystyle \int _{a}^{x}\int _{a}^{s}f(y)\,dy\,ds=\int _{a}^{x}f(y)(x-y)\,dy}$${\displaystyle \sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {m^{2}\,n}{3^{m}\left(m\,3^{n}+n\,3^{m}\right)}}}$${\displaystyle u''+p(x)u'+q(x)u=f(x),\quad x>a}$ ${\displaystyle |{\bar {z}}|=|z|,|({\bar {z}})^{n}|=|z|^{n},\arg(z^{n})=n\arg(z)\,}$${\displaystyle \lim _{z\rightarrow z_{0}}f(z)=f(z_{0})\,}$${\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}$${\displaystyle \phi _{n}(\kappa )=0.033C_{n}^{2}\kappa ^{-11/3},\quad {\frac {1}{L_{0}}}\ll \kappa \ll {\frac {1}{l_{0}}}\,}$${\displaystyle f(x)={\begin{cases}1&-1\leq x<0\\{\frac {1}{2}}&x=0\\1-x^{2}&0<x\leq 1\end{cases}}}$${\displaystyle {}_{p}F_{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!}}\,}$

Leibnizin sarja
${\displaystyle {\frac {\pi }{4}}=\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2k+1}}}$

Eulerin sarja
${\displaystyle {\frac {\pi ^{2}}{6}}=\sum _{k=1}^{\infty }{\frac {1}{k^{2}}}}$

Samankaltainen sarja
${\displaystyle {\frac {\pi ^{2}}{8}}=\sum _{k=0}^{\infty }{\frac {1}{(2k+1)^{2}}}}$

Erilainen sarja
${\displaystyle {\frac {4}{\pi }}=1+{\frac {1}{3+{\frac {4}{5+{\frac {9}{7+{\frac {16}{9+{\frac {25}{11+{\frac {36}{13+...}}}}}}}}}}}}}$

Wallisin tulonlähde

${\displaystyle {\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots ={\frac {\pi }{2}}}$

Joka voidaan kirjoittaa myös näin:

${\displaystyle \prod _{n=1}^{\infty }{\frac {(2n)^{2}}{(2n)^{2}-1}}=\prod _{n=1}^{\infty }{\frac {2n}{2n-1}}\cdot {\frac {2n}{2n+1}}={\frac {\pi }{2}}}$

• 1+1=11
• 6-5=1
• 7 + 7 = 12
• 14 + 14 - 14 x 14 : 14 = 14,14141411414141414...
• π=3