What does laurent series mean?
Definitions for laurent series
lau·rent se·ries
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Wikidata
Laurent series
In mathematics, the Laurent series of a complex function f 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. The Laurent series was named after and first published by Pierre Alphonse Laurent in 1843. Karl Weierstrass may have discovered it first in 1841 but did not publish it at the time. The Laurent series for a complex function f about a point c is given by: where the an are constants, defined by a line integral which is a generalization of Cauchy's integral formula: The path of integration is counterclockwise around a closed, rectifiable path containing no self-intersections, enclosing c and lying in an annulus A in which is holomorphic. The expansion for will then be valid anywhere inside the annulus. The annulus is shown in red in the diagram on the right, along with an example of a suitable path of integration labeled . If we take to be a circle, where, this just amounts to computing the complex Fourier coefficients of the restriction of to . The fact that these integrals are unchanged by a deformation of the contour is an immediate consequence of Stokes' theorem.
Numerology
Chaldean Numerology
The numerical value of laurent series in Chaldean Numerology is: 9
Pythagorean Numerology
The numerical value of laurent series in Pythagorean Numerology is: 4
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"laurent series." Definitions.net. STANDS4 LLC, 2024. Web. 7 May 2024. <https://www.definitions.net/definition/laurent+series>.
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