Power Series

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High Quality Content by WIKIPEDIA articles! Every power series with a positive radius of convergence is analytic on the interior of its region of convergence. All holomorphic functions are complex-analytic. Sums and products of analytic functions are analytic, as are quotients as long as the denominator is non-zero. If a power series with radius of convergence r is given, one can consider analytic continuations of the series, i.e. analytic functions f which are defined on larger sets than { x : x - c r } and agree with the given power series on this set. The number r is maximal in the following sense: there always exists a complex number x with x - c = r such that no analytic continuation of the series can be defined at x.

Weitere Informationen

  • Allgemeine Informationen
    • GTIN 09786130339043
    • Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
    • Sprache Englisch
    • Genre Physik & Astronomie
    • Größe H218mm x B149mm x T17mm
    • Jahr 2010
    • EAN 9786130339043
    • Format Fachbuch
    • ISBN 978-613-0-33904-3
    • Titel Power Series
    • Untertitel Mathematics, Series (mathematics), Taylor Series, Combinatorics, Generating Function, Decimal, Real Number, Number Theory, Geometric Series, Radius of Convergence
    • Gewicht 203g
    • Herausgeber Betascript Publishers
    • Anzahl Seiten 124

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