Polylogarithms pdf
WebWe remark that the present extension from polylogarithms of rational numbers to polylogarithms of algebraic numbers is analogue to the extension made in [1], where Amoroso and Viola obtain good approximation measures for logarithms of algebraic numbers by generalizing a previous method of Viola [5] for logarithms of rational numbers. WebIt appears that the only known representations for the Riemann zeta function ((z) in terms of continued fractions are those for z = 2 and 3. Here we give a rapidly converging continued-fraction expansion of ((n) for any integer n > 2. This is a special case of a more general expansion which we have derived for the polylogarithms of order n, n > 1, by using the …
Polylogarithms pdf
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WebMar 1, 2011 · PDF In this paper we investigate special generalized Bernoulli polynomials that generalize classical Bernoulli polynomials and numbers. ... Keywords: polylogarithms; zeta functions; ... WebMay 18, 2009 · It is convenient to extend the sequence Lin(z) backwards in the manner suggested by (2) and define. Then Li1(z) = – log (l– z ), and Lin(z) is a rational function of …
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 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 …
Webproof of such a relation to some involving only polylogarithms of lower order. As an example we mention 2 relations among trilogarithms which has occurred in our work with C.-H. Sah [6] on the homology of the discrete group Gl(n, C). (See also [14, Section 4].) There the algebraically defined maps L* naturally occurs in expressions of certain ... WebOct 4, 2014 · Nakamura, Wojtkowiak, and the first author showed an explicit formula relating Coleman's p-adic polylogarithms and Wojtkowiak's p-adicétale polylogarithms in [11], [12].
WebAug 24, 2024 · View PDF on arXiv. Save to Library Save. Create Alert Alert. Cite. Share This Paper. 2 Citations. Background Citations. 2. View All. 2 Citations. Citation ... Abstract The values at 1 of single-valued multiple polylogarithms span a certain subalgebra of multiple zeta values. The properties of this algebra are studied from the point ...
WebApr 14, 2024 · The main purpose of this paper is to define multiple alternative q-harmonic numbers, Hnk;q and multi-generalized q-hyperharmonic numbers of order r, Hnrk;q by using q-multiple zeta star values (q-MZSVs). We obtain some finite sum identities and give some applications of them for certain combinations of q-multiple polylogarithms … philip laser machineWebThe Computation of Polylogarithms David C. Wood ABSTRACT The 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 tru finish body shop gastonia ncWebApr 12, 2024 · For m ore about polylogarithms in theory of univalent functions see Ponnusamy and Sabapathy [8], K.Al Shaqsi and M.Daraus [4] and Pon nusamy [9 ]. Now we introducing a function philip lassiter show usaWeband m. When x D0, our result implies the linear independence of polylogarithms of distinct algebraic numbers of arbitrary degree, subject to a metric condition. We give an outline of our proof together with concrete examples of linearly independent polylogarithms. 1. Introduction Let s be a nonnegative integer and 0 x <1 be a rational number. philip larkin your mum and dad poemWebMar 8, 2007 · Download PDF Abstract: We investigate the elliptic analogs of multi-indexed polylogarithms that appear in the theory of the fundamental group of the projective line minus three points as sections of a universal nilpotent bundle with regular singular connection. We use an analytic uniformisation to derive the fundamental nilpotent De … philip larkin this is the versehttp://www.numdam.org/item/ASNSP_2006_5_5_1_1_0.pdf philip laternserWebpolylogarithms can be taken to genus one easily: iterated integrals on genus one allow for a natural shuffle multiplication and an associated coaction or symbol map [31]. Given the existence of the symbol map for elliptic iterated integrals, it is a natural problem to investigate functional relations for elliptic polylogarithms. trufi news