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Q4Section I (General (compulsory))4 of 190

Re-centering the geometric series for 1/z1/z at z=1z=1

Define f:C−{0}→Cf:\mathbf C-\{0\}\to\mathbf C by f(z)=1/zf(z)=1/z. Then the power series expansion of f(z)f(z) about z=1z=1 in the disc {z:∣z−1∣<1}\{z:|z-1|<1\} is:

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