Complex Analysis

Some examples taken from Applied Complex Analysis, by Henrici.
Each of these applets uses the WebEQ parameter.


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Note: click with the right mouse button on any WebEQ equation to bring up a font size control panel.

From p. 421

\int^1_\kappa
\left[\left(1-w^2\right)\left(\kappa^2-w^2\right)\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)

From p. 425

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

From 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}