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Display information for equation id:math.1931.39 on revision:1931

* Page found: Räumliche Isotropie (eq math.1931.39)

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Räumliche Isotropie Eq: math.1931.39

Hash: 9215eba51184eab7d8158f0d7b552e2b

TeX (original user input):

\begin{align}
  & \left( \begin{matrix}
   \cos \phi  & \sin \phi   \\
   -\sin \phi  & \cos \phi   \\
\end{matrix} \right)=\bar{\bar{1}}\sum\limits_{n=0}^{\infty }{\frac{{{\left( -1 \right)}^{n}}}{\left( 2n \right)!}{{\phi }^{2n}}-\bar{\bar{M}}}\sum\limits_{n=0}^{\infty }{\frac{{{\left( -1 \right)}^{n}}}{\left( 2n+1 \right)!}{{\phi }^{2n+1}}} \\
 & =\sum\limits_{n=0}^{\infty }{\frac{1}{\left( 2n \right)!}{{{\bar{\bar{M}}}}^{2n}}{{\phi }^{2n}}-\bar{\bar{M}}}\sum\limits_{n=0}^{\infty }{\frac{1}{\left( 2n+1 \right)!}{{{\bar{\bar{M}}}}^{2n+1}}{{\phi }^{2n+1}}} \\
 & =\exp \left( -\bar{\bar{M}}\phi  \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&\left({\begin{matrix}\cos \phi &\sin \phi \\-\sin \phi &\cos \phi \\\end{matrix}}\right)={\bar {\bar {1}}}\sum \limits _{n=0}^{\infty }{{\frac {{\left(-1\right)}^{n}}{\left(2n\right)!}}{{\phi }^{2n}}-{\bar {\bar {M}}}}\sum \limits _{n=0}^{\infty }{{\frac {{\left(-1\right)}^{n}}{\left(2n+1\right)!}}{{\phi }^{2n+1}}}\\&=\sum \limits _{n=0}^{\infty }{{\frac {1}{\left(2n\right)!}}{{\bar {\bar {M}}}^{2n}}{{\phi }^{2n}}-{\bar {\bar {M}}}}\sum \limits _{n=0}^{\infty }{{\frac {1}{\left(2n+1\right)!}}{{\bar {\bar {M}}}^{2n+1}}{{\phi }^{2n+1}}}\\&=\exp \left(-{\bar {\bar {M}}}\phi \right)\\\end{aligned}}

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MathML (5.947 KB / 601 B) :

\begin{aligned} (\begin{matrix} \cos ϕ & \sin ϕ \\ - \sin ϕ & \cos ϕ \end{matrix}) = \bar{\bar{1}} \sum_{n = 0}^{\infty} \frac{{(- 1)}^{n}}{(2 n)!} ϕ^{2 n} - \bar{\bar{M}} \sum_{n = 0}^{\infty} \frac{{(- 1)}^{n}}{(2 n + 1)!} ϕ^{2 n + 1} \\ = \sum_{n = 0}^{\infty} \frac{1}{(2 n)!} {\bar{\bar{M}}}^{2 n} ϕ^{2 n} - \bar{\bar{M}} \sum_{n = 0}^{\infty} \frac{1}{(2 n + 1)!} {\bar{\bar{M}}}^{2 n + 1} ϕ^{2 n + 1} \\ = \exp (- \bar{\bar{M}} ϕ) \end{aligned}

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Identifiers

$ϕ$

$ϕ$

$ϕ$

$ϕ$

$\bar{\bar{1}}$

$n$

$n$

$n$

$ϕ$

$n$

$\bar{\bar{M}}$

$n$

$n$

$n$

$ϕ$

$n$

$n$

$n$

$\bar{\bar{M}}$

$n$

$ϕ$

$n$

$\bar{\bar{M}}$

$n$

$n$

$\bar{\bar{M}}$

$n$

$ϕ$

$n$

$\bar{\bar{M}}$

$ϕ$

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