CVR17

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Find the residues of f(z)\, at all its isolated singular points and at infinity (if infinity is not a limit point of singular points), where f(z)\, is given by {\frac  {(Log(z))2}{z^{2}+1}}\,

The poles are at z=\pm i\,.

\lim _{{z\to i}}{\frac  {(Log(z))^{2}}{z+i}}={\frac  {(Log(i))^{2}}{2i}}={\frac  {(i\pi /2)^{2}}{2i}}={\frac  {i\pi ^{2}}{8}}\,

\lim _{{z\to -i}}{\frac  {(Log(z))^{2}}{z-i}}={\frac  {(\log -i)^{2}}{-2i}}={\frac  {(-i\pi /2)^{2}}{-2i}}={\frac  {-i\pi ^{2}}{8}}\,


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