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Geometrically, the two Laurent series may have non-overlapping annuli of convergence. Two Laurent series with only finitely many negative terms can be multiplied: algebraically, the sums are all finite; geometrically, these have poles at , and inner radius of convergence 0, so they both converge on an overlapping annulus.
In mathematics, the regular part of a Laurent series consists of the series of terms with positive powers. [1] That is, if = ...
Pierre Alphonse Laurent (18 July 1813 – 2 September 1854) was a French mathematician, engineer, and Military Officer best known for discovering the Laurent series, an expansion of a function into an infinite power series, generalizing the Taylor series expansion. He was born in Paris, France.
The principal part at = of a function = = ()is the portion of the Laurent series consisting of terms with negative degree. [1] That is, = is the principal part of at .If the Laurent series has an inner radius of convergence of , then () has an essential singularity at if and only if the principal part is an infinite sum.
A Laurent polynomial over may be viewed as a Laurent series in which only finitely many coefficients are non-zero. The ring of Laurent polynomials R [ X , X − 1 ] {\displaystyle R\left[X,X^{-1}\right]} is an extension of the polynomial ring R [ X ] {\displaystyle R[X]} obtained by "inverting X {\displaystyle X} ".
In 2D Euclidean field theory, the operator product expansion is a Laurent series expansion associated with two operators. In such an expansion, there are finitely many negative powers of the variable, in addition to potentially infinitely many positive powers of the variable.
Laurence Kerr Olivier, Baron Olivier (/ ˈ l ɒr ə n s ˈ k ɜːr ə ˈ l ɪ v i eɪ / LORR-ənss KUR ə-LIV-ee-ay; 22 May 1907 – 11 July 1989) was an English actor and director.He and his contemporaries Ralph Richardson and John Gielgud made up a trio of male actors who dominated the British stage of the mid-20th century.
Laurent is a French masculine given name of Latin origin. It is used in France , Canada , and other French-speaking countries . The name was derived from the Roman surname Laurentius , which meant "from Laurentum".