Answered: Let f(z)=∑∞n= 0 cn(z - z0)n be a power…

Let f(z)=∑∞n= 0 cn(z - z0)n be a power series with radius of convergence p. Show that for all r < p, using the fundamental theorem of calculus that, ∫∂Dr(z0) f(z) dz = 0.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 50E

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Question

Let f(z)=∑^∞_{n= 0}c_n(z - z₀)ⁿbe a power series with radius of convergence p. Show that for all r < p, using the fundamental theorem of calculus that, ∫_∂Dr(z0)f(z) dz = 0.

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