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Boundary behavior of power series

Teja Koprivc (2018) Boundary behavior of power series. Diploma thesis.

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    Abstract

    This diploma thesis will mostly focus on the problem of convergence of the complex power series. There is a maximum open disk for the power series, which the series converges, however, it is much more complicated to under- stand the convergence at boundary points of this disk and to determine at which points of the boundary has the series has a local holomorphic exten- sion. This thesis includes some interesting examples of the power series on a complex disk and some detailed description of a convergence at boundary points of the disk. For better understanding of the convergence at boundary points, we used and prove Abel’s theorem.

    Item Type: Thesis (Diploma thesis)
    Keywords: power series, uniform convergence, radius of convergence, boundary behavior, convergence tests, Abel’s theorem
    Number of Pages: 28
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    izr. prof. dr. Marko SlaparMentor
    asist. dr. Eva HorvatComentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=12117321)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 5363
    Date Deposited: 24 Sep 2018 11:29
    Last Modified: 28 Aug 2019 11:52
    URI: http://pefprints.pef.uni-lj.si/id/eprint/5363

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