Plone and Math

Simple Examples

<div class="math">
  \int {1\over x}\,dx = \ln(x)+C
</div>

\int {1\over x}\,dx = \ln(x)+C

<div class="math">
  \sum_{i=1}^n i = {n(n+1)\over 2}
</div>

\sum_{i=1}^n i = {n(n+1)\over 2}

<div class="math">
  \left(\, \sum_{k=1}^n a_k b_k \right)^2 
  \le 
  \left(\, \sum_{k=1}^n a_k^2 \right) 
  \left(\, \sum_{k=1}^n b_k^2 \right)
</div>

\left(\, \sum_{k=1}^n a_k b_k \right)^2 \le \left(\, \sum_{k=1}^n a_k^2 \right) \left(\, \sum_{k=1}^n b_k^2 \right)

<div class="math">
  \det\left|\,\matrix{
    c_0    & c_1     & c_2     & \ldots & c_{n\phantom{+1}}\\
    c_1    & c_2     & c_3     & \ldots & c_{n+1} \\
    c_2    & c_3     & c_4     & \ldots & c_{n+2} \\
    \vdots & \vdots  & \vdots  & \ddots & \vdots  \\
    c_n    & c_{n+1} & c_{n+2} & \ldots & c_{2n}
  } \right| \gt 0 
</div>

\det\left|\,\matrix{ c_0 & c_1 & c_2 & \ldots & c_{n\phantom{+1}}\\ c_1 & c_2 & c_3 & \ldots & c_{n+1} \\ c_2 & c_3 & c_4 & \ldots & c_{n+2} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ c_n & c_{n+1} & c_{n+2} & \ldots & c_{2n}} \right| \gt 0 .

Complex Analysis Examples

Some examples taken from Applied Complex Analysis by Henrici,

p. 421

\int^1_\kappa \left[\bigl(1-w^2\bigr)\bigl(\kappa^2-w^2\bigr)\right]^{-1/2} dw = \frac{4}{\left(1+\sqrt{\kappa}\,\right)^2} K \left(\left(\frac{1-\sqrt{\kappa}}{1+\sqrt{\kappa}}\right)^{\!\!2}\right)

p. 425

\mathop{\rm grd} \phi(z) = \left(a+\frac{2d}{\pi}\right) v_\infty\, \overline{f'(z)} = v_\infty \left[ \pi a + \frac{2d}{\pi a + 2dw^{-1/2}(w-1)^{1/2}} \right]^-

p. 455

-\sum^n_{m=1} \left(\,\sum^\infty_{k=1} \frac{ h^{k-1} }{\left(w_m-z_0\right)^2} \right) = \sum^\infty_{k=1} s_k\, h^{k-1}

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