 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-1-course-of-the-university-of-oxford/2013/analysis/6/a/i/solution

a

means that

f

is holomorphic in some punctured disk

0 < ∣ z - a ∣ < r

, while

a

itself is an excluded point or a point where the given function is not holomorphic. There are no other singularities arbitrarily close to

a

f (z) = \sum_{j = - \infty}^{\infty} c_{j} (z - a)^{j} .

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