Representations of analytic functions as infinite products and their application to numerical computations

TY - JOUR

T1 - Representations of analytic functions as infinite products and their application to numerical computations

AU - Mazur, Marcin

AU - Petrenko, Bogdan V.

N1 - Let D be an open disk of radius ≤1 in $\mathbb{C}$ , and let (ϵ n ) be a sequence of ±1. We prove that for every analytic function $f: D \to \mathbb{C}$ without zeros in D, there exists a unique sequence (α n ) of complex numbers such that $f(z) = f(0)\prod_{n=1}^{\infty} (1+\epsilon_{n}z^{n})^{\alpha_{n}}$ for every z∈D.

PY - 2014/1/14

Y1 - 2014/1/14

UR - https://link.springer.com/article/10.1007/s11139-013-9546-3

U2 - 10.1007/S11139-013-9546-3

DO - 10.1007/S11139-013-9546-3

M3 - Article

VL - 34

JO - Ramanujan Journal

JF - Ramanujan Journal

ER -