Polylogarithm
Web, when s 1, … , s k are positive integers and z a complex number in the unit disk. For k = 1, this is the classical polylogarithm Li s (z).These multiple polylogarithms can be defined also in terms of iterated Chen integrals and satisfy shuffle relations.Multiple polylogarithms in several variables are defined for s i ≥ 1 and z i < 1(1 ≤ i ≤ k) by WebOct 8, 1999 · Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider …
Polylogarithm
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Webgives the Nielsen generalized polylogarithm function . Details. Mathematical function, suitable for both symbolic and numerical manipulation.. . . PolyLog [n, z] has a branch cut … Webnthe weight (or transcendentality) of the polylogarithm. Multiple polylogarithms de ned as power series Li n 1;:::;n k(x1;:::;x k) = X 1 p 1<:::
WebInformally, a cluster polylogarithm is a homotopy-invariant iterated integral ż γ ÿ i “ dlogpai 1q ... dlogpai nq ‰ on XsmpCq where for each ithere exists a cluster containing cluster variables ai 1,...,a i n. We call the latter condition cluster adjacency, it was inspired by [DFG18]. Consider the following simplest example. WebOct 24, 2024 · In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Li s (z) of order s and argument z.Only for special …
WebThe polylogarithm function, Li p(z), is defined, and a number of algorithms are derived for its computation, valid in different ranges of its real parameter p and complex argument z. These are sufficient to evaluate it numerically, with reasonable efficiency, in all cases. 1. Definition The polylogarithm may be defined as the function Li p ... WebMar 24, 2024 · The trilogarithm Li_3(z), sometimes also denoted L_3, is special case of the polylogarithm Li_n(z) for n=3. Note that the notation Li_3(x) for the trilogarithm is unfortunately similar to that for the logarithmic integral Li(x). The trilogarithm is implemented in the Wolfram Language as PolyLog[3, z]. Plots of Li_3(z) in the complex …
WebIn mathematics, a polylogarithmic function in n is a polynomial in the logarithm of n , The notation logkn is often used as a shorthand for (log n)k, analogous to sin2θ for (sin θ)2 . …
WebPolylogarithms of Numeric and Symbolic Arguments. polylog returns floating-point numbers or exact symbolic results depending on the arguments you use. Compute the polylogarithms of numeric input arguments. The polylog function returns floating-point numbers. Li = [polylog (3,-1/2), polylog (4,1/3), polylog (5,3/4)] csn financial aid phoneWebThe Polylogarithm package provides C, C++ and Fortran implementations of various polylogarithms, including the real and complex dilogarithm, trilogarithm, and (Standard and Glaisher) Clausen functions. The implementations have been fully tested against the literature and many other implementations and are highly optimized for fast numerical ... eagle tool company kingsford miWebWe associate to a multiple polylogarithm a holomorphic 1-form on the universal abelian cover of its domain. We relate the 1-forms to the symbol and variation matrix and show that the 1-forms naturally define a lift of … eagleton trail challenge 50kWebMar 3, 1997 · We prove a special representation of the polylogarithm function in terms of series with such numbers. Using … Expand. 1. PDF. Save. Alert. Identities Involving Generalized Harmonic Numbers and Other Special Combinatorial Sequences. Huyile Liang; Mathematics. 2012; eagle tool companyWebThe dilogarithm function (sometimes called Euler’s dilogarithm function) is a special case of the polylogarithm that can be traced back to the works of Leonhard Euler. The function re … eagleton school tnWebtween multiple polylogarithm values at Nth roots of unity, Racinet attached to each finite cyclic group G of order N and each group embedding ι : G → C×, a Q-scheme DMRι which associates to each commutative Q-algebra k, a set DMRι(k) that can be decomposed as a disjoint union of sets DMRι λ(k) with λ ∈ k. He also exhibited a Q- csn fire science degree sheetWebThe polylogarithm function is an important function for integration, and finding seemingly complicated sum. Polylogarithm is connected to the infinite geometric progression sum ... csn fine art gallery