. C A ] 9 J ul 1 99 3 Zeilberger A HIGH - SCHOOL ALGEBRA 1 , WALLET - SIZED PROOF , OF THE BIEBERBACH CONJECTURE
نویسنده
چکیده
Weinstein’s[2] brilliant short proof of de Branges’[1] theorem can be made yet much shorter(modulo routine calculations), completely elementary (modulo Löwner theory), self contained(no need for the esoteric Legendre polynomials’ addition theorem), and motivated(ditto), as follows. Replace the text between p. 62, line 7 and p. 63, line 7, by Fact 1 below, and the text between the last line of p.63 and p.64, line 7, by Fact 2 below. FACT 1: Let ft(z) = e z exp( ∑ ∞ k=0 ck(t)z ) where ck(t) are formal functions of t. Let z and w be related by z/(1 − z) = ew/(1 − w). The following formal identity holds. (For any formal Laurent series f(z), CTzf(z) denotes the Constant Term of f(z).)
منابع مشابه
Bieberbach’s conjecture, the de Branges and Weinstein functions and the Askey-Gasper inequality
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