limit for exp(z)

For any complex numberMathworldPlanetmathPlanetmath z, we have


where exp denotes the exponential functionDlmfDlmfMathworldPlanetmathPlanetmath.
Proof: For α0, we have

ln(1+α) =k=1(-1)k-1αkk


(1+zn+o(1n))n = exp(nln(1+zn+o(1n)))
= exp(n(zn+o(1n)+O(1n2)))
= exp(z+o(1)+O(1n))expzforn.
Title limit for exp(z)
Canonical name LimitForExpz
Date of creation 2013-03-22 14:34:54
Last modified on 2013-03-22 14:34:54
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 11
Author mathcam (2727)
Entry type Theorem
Classification msc 30A99