- #1
eaglesmath15
- 7
- 0
Homework Statement
Obtain the Taylor series ez=e Ʃ(z-1)n/n! for 0[itex]\leq(n)[/itex]<[itex]\infty[/itex], (|z-1|<[itex]\infty[/itex]) for the function f(z)=ez by (ii) writing ez=ez-1e.
Homework Equations
Taylor series:
f(z) = Ʃ(1/2\pi/i ∫(f(z)/(z-z0)n+1dz)(z-z0)n
The Attempt at a Solution
The first part of this question called for the Taylor series to be found using the Cauchy Integral shortcut at fn(1), so I assume that this is meant to be solved using the formula for Taylor series as is, but that's where I get stuck. I fill in the Taylor series, and reduce to:
f(z)=e Ʃ(z-1)n∫ez-1/(z-1)n+1}dz
and I have no idea how to get the integral to equal [itex]\stackrel{1}{n!}[/itex], which is what it must in order to equal the original condition.