Laurent series complex analysis examples

  • What is Laurent series in complex analysis?

    8.7: Laurent Series.
    The Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree.
    It may be used to express complex functions in cases where a Taylor series expansion cannot be applied. 8.8: Digression to Differential Equations..

  • What is Laurent's series in complex analysis?

    What is Laurent's Series? Laurent's series, also known as Laurent's expansion, of a complex function f(z) is defined as a representation of that function in terms of power series that includes the terms of negative degree.
    Laurent's series was first published by Pierre Alphonse Laurent in 1843..

  • What is the use of Laurent series in complex analysis?

    The method of Laurent series expansions is an important tool in complex analysis.
    Where a Taylor series can only be used to describe the analytic part of a function, Laurent series allows us to work around the singularities of a complex function.May 15, 2020.

  • A power series with non-negative power terms is called a Taylor series.
    In complex variable theory, it is common to work with power series with both positive and negative power terms.
    This type of power series is called a Laurent series.
  • with the Laurent series f ( z ) = a 0 + a 1 ( z − a ) + a 2 ( z − a ) 2 + . . . + a − 1 ( z − a ) + a − 2 ( z − a ) 2 + . . . .
    As mentioned, this series is convergent in a region ℜ within two concentric circles C 1 and C 2 centered on the point a (see Fig.
May 2, 2023The Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree  Theorem 8.7.1 Laurent seriesNoteExamples of Laurent Series
Laurent's series, also known as Laurent's expansion, of a complex function f(z) is defined as a representation of that function in terms of power series that 

Mathematical series

In calculus, a function series is a series, where the summands are not just real or complex numbers but functions.
Laurent series complex analysis examples
Laurent series complex analysis examples

Expression of a function as an infinite sum of simpler functions

In mathematics, a series expansion is a technique that expresses a function as an infinite sum, or series, of simpler functions.
It is a method for calculating a function that cannot be expressed by just elementary operators.

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