Results 11 to 20 of about 562 (207)
Discrete Polylogarithm Functions [PDF]
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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On Meromorphic Harmonic Functions Associated with the Polylogarithm Function
MathematicsThis paper examines the relationship between the classical polylogarithm function and meromorphic harmonic univalent mappings. Using a convolution operator derived from the polylogarithm function, we define a class of harmonic meromorphic functions and ...
Huda Ali Aldweby
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A construction of the polylogarithm motive [PDF]
Épijournal de Géométrie AlgébriqueClassical polylogarithms give rise to a variation of mixed Hodge-Tate structures on the punctured projective line $S=\mathbb{P}^1\setminus \{0, 1, \infty\}$, which is an extension of the symmetric power of the Kummer variation by a trivial variation.
Clément Dupont, Javier Fresán
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Some New Transformation Properties of the Nielsen Generalized Polylogarithm [PDF]
International Journal of Mathematics and Mathematical Sciences, 2014 Many of the properties of Nielsen generalized polylogarithm Sn,p(z), for example, the special value and the transformation formulas, play important roles in the computation of higher order radiative corrections in quantum electrodynamics.
Nina Shang, Qinghua Feng, Huizeng Qin
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Strong Differential Subordinations Obtained with New Integral Operator Defined by Polylogarithm Function [PDF]
International Journal of Mathematics and Mathematical Sciences, 2014 By using the polylogarithm function, a new integral operator is introduced. Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new ...
K. AL-Shaqsi
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Evaluation of the real parts of polylogarithm expressions containing complex arguments via certain logarithmic integrals [PDF]
Notes on Number Theory and Discrete MathematicsWe consider a polylogarithm expression containing complex arguments, namely 𝓟±(n)=ℜ(Liₙ((1±i)/2)). The central notion of the present paper is to evaluate the real parts of 𝓟±(n) for first four orders, specifically n = 1,2,3, and 4, by constructing ...
Narendra Bhandari
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A Sixteenth-order Polylogarithm Ladder.
Exp. Math., 1992 The mth polylogarithm function is defined by \textLi\sb m(z)=\sum\sp ∞\sbn=1z\sp nn\sp-m. The modified polylogarithm is defined by P\sb m(x)=\textRe\sb m≤ft(\sum\sp m\sbr=02\sp rB\sb r(r!)\sp- 1(\log\vert x\vert)\sp r\textLi\sbm-r(x)\right), where \textRe\sb m is the real part if m is odd, and the imaginary part if m is even.
Cohen, Henri +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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An enhancement of Zagier’s polylogarithm conjecture
Transactions of the American Mathematical Society, 2019 Let m ≥ 2
Nobuo Sato
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Linear Forms in Polylogarithms [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2022 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.
David, Sinnou +2 more
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