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Display information for equation id:math.2382.53 on revision:2382

* Page found: Wahrscheinlichkeitsbegriff (eq math.2382.53)

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Wahrscheinlichkeitsbegriff Eq: math.2386.53

Hash: 06ff4b7ce7834e34c9228ac7df80ca75

TeX (original user input):

\begin{align}
& Z(a)=\left\langle {{e}^{ax}} \right\rangle =\left\langle \sum\limits_{n1,n2...nd=0}^{{}}{{}}\frac{\left( {{\left( {{a}_{1}}x1 \right)}^{n1}}{{\left( {{a}_{2}}x2 \right)}^{n2}}...{{\left( {{a}_{d}}xd \right)}^{nd}} \right)}{n1!n2!...nd!} \right\rangle =\sum\limits_{n1,n2...nd=0}^{{}}{{}}\frac{\left( {{\left( {{a}_{1}} \right)}^{n1}}{{\left( {{a}_{2}} \right)}^{n2}}...{{\left( {{a}_{d}} \right)}^{nd}} \right)}{n1!n2!...nd!}{{M}_{n1..nd}} \\
& a=\left( {{a}_{1}},{{a}_{2}},...,{{a}_{d}} \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&Z(a)=\left\langle {{e}^{ax}}\right\rangle =\left\langle \sum \limits _{n1,n2...nd=0}^{}{}{\frac {\left({{\left({{a}_{1}}x1\right)}^{n1}}{{\left({{a}_{2}}x2\right)}^{n2}}...{{\left({{a}_{d}}xd\right)}^{nd}}\right)}{n1!n2!...nd!}}\right\rangle =\sum \limits _{n1,n2...nd=0}^{}{}{\frac {\left({{\left({{a}_{1}}\right)}^{n1}}{{\left({{a}_{2}}\right)}^{n2}}...{{\left({{a}_{d}}\right)}^{nd}}\right)}{n1!n2!...nd!}}{{M}_{n1..nd}}\\&a=\left({{a}_{1}},{{a}_{2}},...,{{a}_{d}}\right)\\\end{aligned}}

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\begin{aligned} Z (a) = ⟨ e^{a x} ⟩ = ⟨ \sum_{n 1, n 2 . . . n d = 0}^{} \frac{({(a_{1} x 1)}^{n 1} {(a_{2} x 2)}^{n 2} . . . {(a_{d} x d)}^{n d})}{n 1! n 2! . . . n d!} ⟩ = \sum_{n 1, n 2 . . . n d = 0}^{} \frac{({(a_{1})}^{n 1} {(a_{2})}^{n 2} . . . {(a_{d})}^{n d})}{n 1! n 2! . . . n d!} M_{n 1 . . n d} \\ a = (a_{1}, a_{2}, . . ., a_{d}) \end{aligned}

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In Mathematica:

Identifiers

$Z$

$a$

$e$

$a$

$x$

$n$

$n$

$n$

$d$

$a_{1}$

$x$

$n$

$a_{2}$

$x$

$n$

$a_{d}$

$x$

$d$

$n$

$d$

$n$

$n$

$n$

$d$

$n$

$n$

$n$

$d$

$a_{1}$

$n$

$a_{2}$

$n$

$a_{d}$

$n$

$d$

$n$

$n$

$n$

$d$

$M$

$n$

$n$

$d$

$a$

$a_{1}$

$a_{2}$

$a_{d}$

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