 By Miller G. A.

Similar mathematics books

This text discusses a few tools of describing and bearing on mathematical items and of constantly and unambiguously signaling the logical constitution of mathematical arguments.

Extra resources for Arithmetization in the History of Mathematics

Example text

2a, it suffices to estimate P(a; 2r) lID9! IIp(0;,) for each pair a,r such that X. Then, by ii), we see that v, ID9f(1')l If IIP(b;r) Vt llflIP(a;2r) ror each b e P(a; r), and it follows that lID9! IIP(o;r) II! IIP(o. 3, we want to show that a function is holomorphic 1ff it can be represented locally by its Taylor series (Weierstrass's definition of holomorphic functions). 6 Remark. 6 Prop. 9]. Function Theory on Domains in 14 ii) Jf,. iii) f, and converges in I converges in (P(X) to a limit that is independent of the order of summation.

Hint: assume that 0 E then there exist a1,b,c R such that <0; use the function f(z) E. 12g. 9). (a1 — lb1):1 I <1z2 I < 0 1 } is a domain of holomorphy (hint: (X) for 0€ R; for E. 62 b). § 12 A Supplement: Further Extension Theorems for Holomorphic Functions Here we discuss some more consequences of Thullen's Lemma; Proposition 12 A. 3 can serve as motivation for sections 13 and 14. We understand a complex disk D in X a CN to be a set of the form with and din Ca; we also write bd D = d + S' For X sion of ba IR denote the (uniquely determined [Co X.

Ia'I. //) If a E x 0 C", we have that then, with the canonical projection pr: C" —. a multi-index pEN1 can be determined so that