Resurgence of the fractional polylogarithms
نویسندگان
چکیده
منابع مشابه
Resurgence of the Fractional Polylogarithms
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 presentation, we show that the fractional polylogarithms are multivalued analytic functions in the complex plane minus 0 and 1. For non-integer values of α, we prove the analytic continuation, compute the...
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 کاملRelations 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 کاملTowards Multiple Elliptic Polylogarithms
Contents 1. Introduction 1 1.1. History and motivation 1 1.2. What we do 3 1.3. Plan of the article 3 1.4. Conventions and notations 4 2. The De Rham fundamental groupoid of a punctured elliptic curve 5 2.1. Nilpotent vector bundles 5 2.2. Nilpotent connections with simple poles at the origin 6 3. A universal flat connection over the upper-half plane 10 3.1. Combinatorial conventions and lemmas...
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: Mathematical Research Letters
سال: 2009
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2009.v16.n5.a5