Laurent Decomposition of Functions on an Annulus in Complex Analysis
This concept establishes that a function analytic on an annulus can be decomposed into a sum of two functions—one analytic on the inner disk, one analytic outside a smaller disk—via a contour-integration argument using the Cauchy integral formula, and uses this decomposition to derive the Laurent series: a doubly-infinite power series in (z − z₀) with both positive and negative exponents, whose coefficients are given by a Cauchy-type integral formula. It belongs to complex analysis, generalizing Taylor series expansion to functions with singularities, and sits within the theory of analytic functions on annular domains.
Laurent Decomposition of Functions on an Annulus in Complex Analysis
This concept establishes that a function analytic on an annulus can be decomposed into a sum of two functions—one analytic on the inner disk, one analytic outside a smaller disk—via a contour-integra…