HPL, a Mathematica implementation of the harmonic polylogarithms
نویسندگان
چکیده
منابع مشابه
HPL, a Mathematica implementation of the harmonic polylogarithms
In this paper, we present an implementation of the harmonic polylog-arithm of Remiddi and Vermaseren [1] for Mathematica. It contains an implementation of the product algebra, the derivative properties, series expansion and numerical evaluation. The analytic continuation has been treated carefully, allowing the user to keep the control over the definition of the sign of the imaginary parts. Man...
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 کاملExtension of HPL to complex arguments
In this paper we describe the extension of the Mathematica package HPL to treat harmonic polylogarithms of complex arguments. The harmonic polylogarithms have been introduced by Remiddi and Vermaseren [1] and have many applications in high energy particle physics.
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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 کاملHarmonic polylogarithms for massive Bhabha scattering
Oneand two-dimensional harmonic polylogarithms, HPLs and GPLs, appear in calculations of multi-loop integrals. We discuss them in the context of analytical solutions for two-loop master integrals in the case of massive Bhabha scattering in QED. For the GPLs we discuss analytical representations, conformal transformations, and also their transformations corresponding to relations between master ...
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ژورنال
عنوان ژورنال: Computer Physics Communications
سال: 2006
ISSN: 0010-4655
DOI: 10.1016/j.cpc.2005.10.008