Let h and g be differentiable at z0 and g(z0) = 0. Suppose

Chapter 22, Problem 22.30

(choose chapter or problem)

Let h and g be differentiable at z0 and g(z0) = 0. Suppose h has a zero of order 2 at z0. Show that Res(g(z)/h(z),z0) = 2g (z0) h(z0) 2 3 g(z0)h(3) (z0) (h(z0))2 . Hint: Use Theorem 22.6. Begin by writing h(z) = (z z0)2 (z) where (z0) = 0.

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