## Weierstrass’ proof of the Lindemann-Weierstrass Theorem (Part 3 of 3)

In part 3 of his 1885 paper, Weierstrass proved the theorem, which in the form stated by him is: if each of z1, … , zn is algebraic and distinct, and A1, … , An are algebraic then

$A_1e^{z_1}+ ... + A_ne^{z_n}$

cannot be zero unless all of A1, … , An are zero.

In the attached pdf (revised on 6 Aug 2013 – I am grateful to Fang Sun for pointing out a problem with the original which is addressed in this revision), I reproduce part 3 of Weierstrass’ paper, with some minor modifications and some added explanation.