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Math examples


$\displaystyle \phi(\lambda)$ $\textstyle =$ $\displaystyle \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty}
\exp \left( u \ln u + \lambda u \right ) du \hspace{1cm}\mbox{for } c \geq 0$ (1)
$\displaystyle \lambda$ $\textstyle =$ $\displaystyle \frac{\epsilon -\bar{\epsilon} }{\xi}
- \gamma' - \beta^2 - \ln \frac{\xi} {E_{\rm max}}$ (2)
$\displaystyle \gamma$ $\textstyle =$ $\displaystyle 0.577215\dots \mathrm{\hspace{5mm}(Euler's\ constant)}$ (3)
$\displaystyle \gamma'$ $\textstyle =$ $\displaystyle 0.422784\dots = 1 - \gamma$ (4)
$\displaystyle \epsilon , \bar{\epsilon}$ $\textstyle =$ $\displaystyle \mbox{actual/average energy loss}$ (5)

Since 2 and 6 hold for arbitrary $\delta\mathbf{c}$-vectors, it is clear that $\mathcal{N}(A) = \mathcal{R}(B)$ and that when $y=B(x)$ one has...
...the Pythagorians knew infinitely many solutions in integers to $a^2+b^2=c^2$. That no non-trivial integer solutions exist for $a^n+b^n=c^n$ with integers $n>2$ has long been suspected (Fermat, c.1637). Only during the current decade has this been proved (Wiles, 1995).


$\displaystyle V \mathbf{\pi}^{sr}$ $\textstyle =$ $\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i
+ \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right>$ (6)
  $\textstyle =$ $\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i
+ \sum_{i}\sum_{j>i}\...
... j\beta}
- \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right>$  



Subsections

Michel Goossens
1999-03-30