Complex Analysis: Theory and Applications · Problem 7.2.4

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · taylor-series

Problem

Let

f(z) = \dfrac{\sin z}{z}

and set

f(0) = 1

. ((a)) Explain why

f

is analytic at

z = 0

. ((b)) Find the Maclaurin series for

f(z)

. ((c)) Find the Maclaurin series for

g(z) = \displaystyle\int_C f(\zeta)\,d\zeta

, where

C

is the straight-line segment from

0

z