mathematics, the Laurent series of a complex function f ( z ) {\displaystyle f(z)} is a representation of that function as a power series which includes...

power series Puiseux series are an extension of formal Laurent series, allowing fractional exponents Rational series Ring of restricted power series The...

Look up Laurent or laurent in Wiktionary, the free dictionary. Laurent may refer to: Laurent (name), a French masculine given name and a surname Saint...

independent meanings but usually refers to the negative-power portion of the Laurent series of a function. The principal part at z = a {\displaystyle z=a} of a...

be calculated by finding Laurent series expansions, and one can define the residue as the coefficient a−1 of a Laurent series. The concept can be used...

formal power series is also a differential algebra, with differentiation performed term-by-term. Laurent series generalize power series by admitting terms...

variable x; see Laurent series. For example, f (x) = e−1/x2 can be written as a Laurent series. The generalization of the Taylor series does converge to...

Maclaurin series of f is its Taylor series about x 0 = 0 {\displaystyle x_{0}=0} . A Laurent series is a generalization of the Taylor series, allowing...

Laurent series Auguste Laurent (1807–1853), French chemist Christian Laurent, French engineer Joseph Jean Pierre Laurent, a French astronomer Laurent...

of Dales and Woodin. Since a Taylor series evaluated with a Laurent series as its argument is still a Laurent series, the system can be used to do calculus...

Alphonse Laurent (18 July 1813 – 2 September 1854) was a French mathematician, engineer, and Military Officer best known for discovering the Laurent series, an...

Puiseux series becomes a Laurent series in an nth root of the indeterminate. For example, the example above is a Laurent series in x 1 / 6 . {\displaystyle...

of order one at s = 1. It can therefore be expanded as a Laurent series about s = 1; the series development is then ζ ( s ) = 1 s − 1 + ∑ n = 0 ∞ γ n n...

In mathematics, a Laurent polynomial (named after Pierre Alphonse Laurent) in one variable over a field F {\displaystyle \mathbb {F} } is a linear combination...

residue Res(f, c) of f at c is the coefficient a−1 of (z − c)−1 in the Laurent series expansion of f around c. Various methods exist for calculating this...

cosine series Fourier transform Gibbs phenomenon Half range Fourier series Laurent series – the substitution q = eix transforms a Fourier series into a...

x^{-1}+1+x^{1}+x^{2}+\cdots } is not considered a power series (although it is a Laurent series). Similarly, fractional powers such as x 1 2 {\textstyle...

Qa,t(z) is solved from the product of P by the principal part of the Laurent series of f at a: It is proportional to the relevant Frobenius covariant. Then...

powers of integers. The Laurent series expansion can be used to define generalized Stieltjes constants that occur in the series ζ ( s , a ) = 1 s − 1 +...

starred in the Netflix mini-series Class Act (original name "Tapie") as the French businessman and politician Bernard Tapie. "Laurent Lafitte maître du Festival...

power series (in which k ≥ 0). Since any Laurent series is a fraction of a power series divided by a power of x (as opposed to an arbitrary power series),...

{\displaystyle z_{0},} a nonzero meromorphic function f is the sum of a Laurent series with at most finite principal part (the terms with negative index values):...

conjugation), then the resulting ring of Laurent series is a noncommutative division ring known as a skew Laurent series ring; if σ = id then it features the...

recurrence relations. The field involves bijections, power series and formal laurent series. Gessel, Ira M.; Stanley, Richard P. (1995), "Algebraic enumeration"...

(ln) from BetterExplained "Taylor series of 1 / (1 - r/200)". WolframAlpha. Retrieved January 3, 2025. "Laurent series of ln(2) / ln(1 + r/100)". WolframAlpha...

the polynomial terms contributed are exactly the regular part of the Laurent series up to z p {\displaystyle z^{p}} . For the other poles λ k {\displaystyle...

Louis Stephen St. Laurent PC CC QC (French: [lwi sɛ̃ lɔʁɑ̃]; February 1, 1882 – July 25, 1973) was a Canadian lawyer and politician who served as the...

specific instance of a Laurent series, where the sequence of numbers under investigation is interpreted as the coefficients in the (Laurent) expansion of an...

Ellenborough (series 5) Dan O'Keefe as Coldbath Prison Guard (series 5) Don Gallagher as Vicar (series 5) Zachary Fall as Laurent (series 5) Nico Rogner...

Mélanie Laurent (French pronunciation: [melani loʁɑ̃] ; born 21 February 1983) is a French actress and filmmaker. The recipient of two César Awards and...