Branch point | Mathematics, Complex analysis, Multivalued function, Continuous function, Arbitrarily large, Riemann surface, Analytic continuation, Monodromy, Essential singularity, Geometric function theory

Frederic P. Miller (u. a.)

ISBN 10: 6130621175 / ISBN 13: 9786130621179

Published by OmniScriptum, 2026

About this Item

Branch point | Mathematics, Complex analysis, Multivalued function, Continuous function, Arbitrarily large, Riemann surface, Analytic continuation, Monodromy, Essential singularity, Geometric function theory | Frederic P. Miller (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130621179 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.

Seller Inventory # 101332067

Bibliographic Details

• Title: Branch point | Mathematics, Complex analysis, Multivalued function, Continuous function, Arbitrarily large, Riemann surface, Analytic continuation, Monodromy, Essential singularity, Geometric function theory
• Publisher: OmniScriptum
• Publication Date: 2026
• Language: English
• ISBN 10: 6130621175
• ISBN 13: 9786130621179
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 5D millimeters 220 millimeters width by 150 millimeters height by 5 millimeters depth
• Weight: 125 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point (Ablowitz & Fokas 2003, p. 46). Multi-valued functions are rigorously studied using Riemann surfaces, and the formal definition of branch points employs this concept. Branch points fall into three broad categories: algebraic branch points, transcendental branch points, and logarithmic branch points. Algebraic branch points most commonly arise from functions in which there is an ambiguity in the extraction of a root, such as solving the equation z = w2 for w as a function of z. Here the branch point is the origin, because the analytic continuation of any solution around a closed loop containing the origin will result in a different function: there is non-trivial monodromy. Despite the algebraic branch point, the function w is well-defined as a multiple-valued function and, in an appropriate sense, is continuous at the origin.