Reduction of multiple harmonic sums and harmonic polylogarithms
نویسندگان
چکیده
منابع مشابه
Reduction of Multiple Harmonic Sums and Harmonic Polylogarithms
The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index calss rather than on their value. We show how to find a basis of the associated algebra. The length of the basis l is found to be ≤ 1/d, where d is the depth of the su...
متن کاملAnalytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
In recent three–loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short S-sums) arise. They are characterized by rational (or real) numerator weights also different from ±1. In this article we explore the algorithmic and analytic properties of these sums systematically. We wo...
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 کاملHarmonic Sums, Polylogarithms, Special Numbers, and their Generalizations
In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops. These quantities are elements of stuffle and shuffle algebras implying algebraic relations being widely independent of the special quantities considered. They...
متن کاملHarmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin transforms of Poincaré– iterated integrals including denominators of higher cyclotomic polynomials. We derive the cyclotomic harmonic polylogarithms and harmo...
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: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
سال: 2004
ISSN: 0168-9002
DOI: 10.1016/j.nima.2004.07.101