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Question

Mathematics Question on Power series solutions for ordinary points

In the neighborhood of z = 1, the function f(z) has a power series expansion of the form f(z) = 1+(1-z)+(1-z)2 + .... then f(z) is

A

1z\frac{1}{z}

B

−1z−2\frac{-1}{z-2}

C

12z−1\frac{1}{2z-1}

D

z−1z+1\frac{z-1}{z+1}

Answer

1z\frac{1}{z}

Explanation

Solution

The correct answer is(A): 1z\frac{1}{z}