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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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Created: 14 Mar 2004
Last modified: Mar 15, 2009 1:02:08 PM
Comments to: dpvc@union.edu
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