Math examples

$$\phi \lambda {\frac{1}{2 \pi i}} \int^{c+i\infty}_{c-i\infty} \left(\vphantom{ u \ln u + \lambda u }\right. \lambda \left.\vphantom{ u \ln u + \lambda u }\right) \geq$$ = (1)

$$\lambda {\frac{\epsilon -\bar{\epsilon} }{\xi}} \gamma{^\prime} \beta^{2}_{} {\frac{\xi}{E_{\rm max}}}$$ = (2)

$$\gamma$$ = 0.577215...   (Euler's constant) (3)

$$\gamma{^\prime} \gamma$$ = (4)

$$\epsilon \bar{\epsilon}$$ = actual/average energy loss (5)

Since 2 and 6 hold for arbitrary $\delta$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 a² + b² = c². That no non-trivial integer solutions exist for aⁿ + bⁿ = cⁿ with integers n > 2 has long been suspected (Fermat, c.1637). Only during the current decade has this been proved (Wiles, 1995).

$$\pi \left<\vphantom{ \sum_i M_i \mathbf{V}_i \mathbf{V}_i + \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}}\right. \sum_{i}^{} \sum_{i}^{} \sum_{j>i}^{} \left.\vphantom{ \sum_i M_i \mathbf{V}_i \mathbf{V}_i + \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}}\right>$$ = (6)

$$\left<\vphantom{ \sum_i M_i \mathbf{V}_i \mathbf{V}_i + \sum_{i}\... ...j\beta} - \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} }\right. \sum_{i}^{} \sum_{i}^{} \sum_{j>i}^{} \sum_{\alpha}^{} \sum_{\beta}^{} \alpha \beta \alpha \beta \sum_{i}^{} \sum_{\alpha}^{} \alpha \alpha \left.\vphantom{ \sum_i M_i \mathbf{V}_i \mathbf{V}_i + \sum_{i}\... ...j\beta} - \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} }\right>$$ =