Results 11 to 20 of about 813 (211)
Linear Forms in Polylogarithms [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2020 Let $r, \,m$ be positive integers. Let $x$ be a rational number with $0 \le x <1$. Consider $Φ_s(x,z) =\displaystyle\sum_{k=0}^{\infty}\frac{z^{k+1}}{{(k+x+1)}^s}$ the $s$-th Lerch function with $s=1, 2, \cdots, r$. When $x=0$, this is a polylogarithmic function.
Sinnou David +2 more
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Dispersion braiding and band knots in plasmonic arrays with broken symmetries. [PDF]
Nanophotonics, 2023 Abstract Periodic arrays can support highly nontrivial modal dispersion, stemming from the interplay between localized resonances of the array elements and distributed resonances supported by the lattice. Recently, intentional defects in the periodicity, i.e., broken in situ symmetries, have been attracting significant attention as a powerful degree of
Yin S, Alù A.
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GENERALIZED FINITE POLYLOGARITHMS [PDF]
Glasgow Mathematical Journal, 2020 AbstractWe introduce a generalization ${\rm{\pounds}}_d^{(\alpha)}(X)$ of the finite polylogarithms ${\rm{\pounds}}_d^{(0)}(X) = {{\rm{\pounds}}_d}(X) = \sum\nolimits_{k = 1}^{p - 1} {X^k}/{k^d}$ , in characteristic p, which depends on a parameter α.
Marina Avitabile, Sandro Mattarei
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Clean Single-Valued Polylogarithms [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 We define a variant of real-analytic polylogarithms that are single-valued and that satisfy ''clean'' functional relations that do not involve any products of lower weight functions. We discuss the basic properties of these functions and, for depths one and two, we present some explicit formulas and results.
Charlton, S. ; https://orcid.org/0000-0002-2815-1885 +2 more
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International Journal of Modern Physics A, 2000 The harmonic polylogarithms (hpl's) are introduced. They are a generalization of Nielsen's polylogarithms, satisfying a product algebra (the product of two hpl's is in turn a combination of hpl's) and forming a set closed under the transformation of the arguments x=1/z and x=(1-t)/(1+t). The coefficients of their expansions and their Mellin transforms
Remiddi, Ettore +1 more
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Tempering the polylogarithm [PDF]
, 2006 Supported by the DARPA FunBio ...
Charles L. Epstein, Jack Morava
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Discrete Polylogarithm Functions
Tatra Mountains Mathematical Publications, 2023 Abstract We investigate a discrete analogue of the polylogarithm function. Difference and summation relations are obtained, as well as its connection to the discrete hypergeometric series.
Cuchta, Tom, Freeman, Dallas
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Cluster Polylogarithms I: Quadrangular Polylogarithms
, 2022 We suggest a definition of cluster polylogarithms on an arbitrary cluster variety and classify them in type $A$. We find functional equations for multiple polylogarithms which generalize equations discovered by Abel, Kummer, and Goncharov to an arbitrary weight. As an application, we prove a part of the Goncharov depth conjecture in weight six.
Matveiakin, Andrei, Rudenko, Daniil
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Elliptic polylogarithms and basic hypergeometric functions [PDF]
The European Physical Journal C, 2017 Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
Giampiero Passarino
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Space Charge Region beyond the Abrupt Approximation
physica status solidi (b), Volume 260, Issue 11, November 2023., 2023 An analytical approximation for the potential, electrical field and charge density in a space charge (depletion) region is found. Good agreement is found with the (numerically) exact solution. The problem of the potential, electrical field and charge density in a space charge region is revisited.
Marius Grundmann
wiley +1 more source