Weierstrass’ proof of the Lindemann-Weierstrass Theorem (Part 2 of 3)

In part 2 of his 1885 paper, Weierstrass reproduced Lindemann’s proof that if z is algebraic,

e^z+1

is not zero.

Weierstrass’ proof of Lindemann’s result is concise and elegant, while still displaying its origins in Hermite’s ground-breaking proof that e is transcendental.  This contrasts with some of the ‘simplifications’ that have followed, for example the surprisingly cumbersome treatment given by Hardy and Wright.

In the attached pdf (updated 25 July 2013), I reproduce part 2 of Weierstrass’ paper, with some minor modifications and some added material on symmetric polynomials.  The latter draws on the description of Waring’s method in Tignol’s book ‘Galois’ Theory of Algebraic Equations’.

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