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

Marcin Mazur; Bogdan V. Petrenko

doi:10.1007/S11139-013-9546-3

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

Marcin Mazur
, Bogdan V. Petrenko

Eastern Illinois University

Binghamton University

Producción científica › revisión exhaustiva

Idioma original	American English
Publicación	Ramanujan Journal
Volumen	34
DOI	https://doi.org/10.1007/S11139-013-9546-3
Estado	Published - ene 14 2014

Disciplines

Mathematics
Discrete Mathematics and Combinatorics
Number Theory

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10.1007/S11139-013-9546-3Licencia: Unspecified

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

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title = "Representations of analytic functions as infinite products and their application to numerical computations",

author = "Marcin Mazur and Petrenko, \{Bogdan V.\}",

note = "Let D be an open disk of radius ≤1 in \$\textbackslash{}mathbb\{C\}\$ , and let (ϵ n ) be a sequence of ±1. We prove that for every analytic function \$f: D \textbackslash{}to \textbackslash{}mathbb\{C\}\$ without zeros in D, there exists a unique sequence (α n ) of complex numbers such that \$f(z) = f(0)\textbackslash{}prod\_\{n=1\}\textasciicircum{}\{\textbackslash{}infty\} (1+\textbackslash{}epsilon\_\{n\}z\textasciicircum{}\{n\})\textasciicircum{}\{\textbackslash{}alpha\_\{n\}\}\$ for every z∈D.",

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day = "14",

doi = "10.1007/S11139-013-9546-3",

language = "American English",

volume = "34",

journal = "Ramanujan Journal",

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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 -