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.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


%d bloggers like this: