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Power Series and Holomorphic Functions

Let f(z) be holomorphic in the region |z|<=R with power series expansion
f(z)=sum(n=0 to infinity) a_nz^n. Let the partial sum of the series be defined as
s_N(z)=sum(n=0 to N) a_nz^n
Show that for |z|less than R we have s_n(z)= 1/i2pi(integral over |w|=R of f(w)[(w^N+1 - z^N+1)/(w-z)]dw/w^N+1)

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Power Series and Holomorphic Functions are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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