Analytic Functions and Zeros at Infinity in Complex Analysis
This concept extends analyticity and zero-order concepts to the point at infinity in complex analysis: a function f is analytic at infinity if f(1/z) is analytic at z = 0, yielding a Laurent-type expansion in powers of 1/z valid outside a disk. It also formalizes zeros of analytic functions (order n at a finite point or at infinity) and proves the key structural theorem that the zeros of a non-identically-zero analytic function are always isolated and of finite order — a rigidity property with no real-analysis counterpart.
Analytic Functions and Zeros at Infinity in Complex Analysis
This concept extends analyticity and zero-order concepts to the point at infinity in complex analysis: a function f is analytic at infinity if f(1/z) is analytic at z = 0, yielding a Laurent-type exp…