Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A First Course in Complex AnalysisResidues

A First Course in Complex Analysis: Residues [Suppose f(z) has an isolated singularity at z0. Then it has a Laurent series expansion around z0, that converges on the region 0 < |z — z0|< R, for some constant R > 0: (7.1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\matrix{ {f\left( z \right) = \sum\limits_{n \in Z} {{a_n}{{\left( {z - {z_0}} \right)}^n},} }{{\rm{where}}}{{a_n} = {1 \over {2\pi i}}\oint_C {{{f\left( z \right)} \over {{{\left( {z - {z_0}} \right)}^{n + 1}}}}dz,} } \cr } $$\end{document}] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A First Course in Complex AnalysisResidues

Download PDF
20 pages

Loading next page...
 
/lp/springer-journals/a-first-course-in-complex-analysis-residues-mtvYMczRoP

References (0)

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2022
ISBN
978-3-031-79171-0
Pages
169 –189
DOI
10.1007/978-3-031-79176-5_7
Publisher site
See Chapter on Publisher Site

Abstract

[Suppose f(z) has an isolated singularity at z0. Then it has a Laurent series expansion around z0, that converges on the region 0 < |z — z0|< R, for some constant R > 0: (7.1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\matrix{ {f\left( z \right) = \sum\limits_{n \in Z} {{a_n}{{\left( {z - {z_0}} \right)}^n},} }{{\rm{where}}}{{a_n} = {1 \over {2\pi i}}\oint_C {{{f\left( z \right)} \over {{{\left( {z - {z_0}} \right)}^{n + 1}}}}dz,} } \cr } $$\end{document}]

Published: Jan 1, 2022

There are no references for this article.