منابع مشابه
Relations for Nielsen polylogarithms
Polylogarithms appear in many diverse fields of mathematics. Herein, we investigate relations amongst Nielsen polylogarithms, both generic and at special arguments including the sixth roots of unity. The relations are explicitly exhibited in the case of low weights. All of this work relies heavily on symbolic and numeric computation. For use in applications all results are implemented and acces...
متن کاملDouble Shuffle Relations of Special Values of Multiple Polylogarithms
In this paper we shall study the special values of multiple polylogarithms atmth roots of unity, called multiple polylogarithmic values (MPVs) of depth m. These objects are generalizations of multiple zeta values and alternating Euler sums. Our primary goal is to investigate the relations between the special values by using (extended) double shuffle relations. In particular we want to know for ...
متن کاملRelations for Multiple Zeta Values and Mellin Transforms of Multiple Polylogarithms
In this paper the relationship between the Ohno relation and multiple polylogarithms are discussed. Using this relationship, the algebraic reduction of the Ohno relation is given.
متن کاملHarmonic Polylogarithms
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 are harmonic sums. AMS(1991) subject cl...
متن کاملMultiple Polylogarithms: An Introduction
when s1, . . . , sk are positive integers and z a complex number in the unit disk. For k = 1, this is the classical polylogarithm Lis (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 si ≥ 1 and |zi | < 1(1 ≤ i ≤ k) by Li(s1,...,sk)(z1, . . . , zk) = ∑ n1>n2>···>n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2015
ISSN: 0021-9045
DOI: 10.1016/j.jat.2013.07.003