Polylogarithms pdf
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 … WebElliptic polylogarithms are multi-valued analytic functions on a punctured ellip-tic curve. We realize the elliptic curve as the quotient of C by lattice L= Z˝ Z. Hence these functions can be described as functions on CnZ˝ Z 3. De nition 1.2 Elliptic …
Polylogarithms pdf
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WebMar 3, 1997 · PDF. View 2 excerpts, references background; Save. Alert. Bernoulli numbers and polynomials of arbitrary complex indices. P. Butzer, M. Hauss, M. Leclerc; ... Nielsen's generalized polylogarithms. K. S. Kölbig; Mathematics. 1986; Properties (in particular functional relations and special values) of the functions \[\begin{gathered ... 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 ...
WebJun 12, 2014 · PDF Many of the properties of Nielsen generalized polylogarithm S n, p (z), for example, the special value and the transformation formulas, play... Find, read and cite all the research you ...
WebFeb 11, 2024 · Download PDF Abstract: For an integer n>2 we define a polylogarithm, which is a holomorphic function on the universal abelian cover of C-{0,1} defined modulo (2 pi i)^n/(n-1)!. We use the formal properties of its functional relations to define groups lifting Goncharov's Bloch groups of a field F, and show that they fit into a complex lifting … WebMar 1, 2011 · PDF In this paper we investigate special generalized Bernoulli polynomials that generalize classical Bernoulli polynomials and numbers. ... Keywords: polylogarithms; zeta functions; ...
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 …
WebWe prove linear independence of indefinite iterated Eisenstein integrals over the fraction field of the ring of formal power series Z[[q]]. Our proof relies on a general criterium for linear independence of iterated integrals, which has been established by Deneufchâtel, Duchamp, Minh and Solomon. As a corollary, we obtain C-linear independence of indefinite iterated … fishing equipment anatomyWebobtain a representation of polylogarithms which will be single valued on the cut plane. For example, for the dilogarithm we obtain Li 2(z) = Z z 0 ln(1 u) u du for z2C (1;1): 6. The … fishing epsomhttp://people.mpim-bonn.mpg.de/stavros/publications/resurgencepolylogarithms.pdf can be invoked concurrently autosarWebKey words: Polylogarithms, modular forms. Introduction The notion of the elliptic polylogarithm functions as a natural generalization of the usual polylogarithms was … fishing equipment bruneiWebAbstract. The fractional polylogarithms, depending on a complex parameter α, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series into an integral presen-tation, we show that the fractional polylogarithms are multivalued analytic functions in the complex plane minus 0 and 1. can be in truck camper when not in truckWebPOLYLOGARITHMS AND POLY-BERNOULLI POLYNOMIALS Abdelmejid BAYAD and Yoshinori HAMAHATA (Received 18 February 2010) Abstract. In this paper we investigate special generalized Bernoulli polynomials that can be knitted word stacksWebThis paper extends tools developed by Crandall (2012) 16 to provide robust, high-precision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to the corresponding computation of the Hurwitz zeta ... fishing equipment auction