Bookcover of Branch point
Booktitle:

Branch point

Alphascript Publishing (2010-09-16 )

Books loader

Omni badge eligible for voucher
ISBN-13:

978-613-0-62117-9

ISBN-10:
6130621175
EAN:
9786130621179
Book language:
English
Blurb/Shorttext:
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.
Publishing house:
Alphascript Publishing
Website:
https://www.alphascript-publishing.com/
Edited by:
Frederic P. Miller, Agnes F. Vandome, John McBrewster
Number of pages:
72
Published on:
2010-09-16
Stock:
Available
Category:
Analysis
Price:
29.00 €
Keywords:
analysis, function, Arbitrarily, Surface, Continuation, singularity, Geometric

Books loader

Newsletter

Adyen::amex Adyen::mc Adyen::visa Adyen::cup Adyen::unionpay Paypal Wire Transfer

  0 products in the shopping cart
Edit cart
Loading frontend
LOADING