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III

We report on results for the heavy flavor contributions to F2(x,Q ) in the limit Q ≫ m at NNLO. By calculating the massive 3–loop operator matrix elements, we account for all but the power suppressed terms in m/Q. Recently, the calculation of fixed Mellin moments of all 3–loop massive operator matrix elements has been finished. We present new all–N results… (More)

- Jakob Ablinger, Johannes Blümlein, Carsten Schneider
- ArXiv
- 2011

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… (More)

- Jakob Ablinger, Johannes Blümlein, Carsten Schneider
- ArXiv
- 2013

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… (More)

- Jakob Ablinger, Johannes Blümlein, Mark Round, Carsten Schneider
- ArXiv
- 2012

Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+ ε-dimensional Minkowski space, can be transformed to multi-integrals or multisums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the… (More)

- Jakob Ablinger, Arnd Behring, Johannes Blümlein, Abilio De Freitas, A. von Manteuffel, Carsten Schneider
- Computer Physics Communications
- 2016

Three loop ladder and V-topology diagrams contributing to the massive operator matrix element AQg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained… (More)

- Jakob Ablinger
- ArXiv
- 2014

This paper summarizes the essential functionality of the computer algebra package HarmonicSums. On the one hand HarmonicSums can work with nested sums such as harmonic sums and their generalizations and on the other hand it can treat iterated integrals of the Poincaré and Chen-type, such as harmonic polylogarithms and their generalizations. The interplay of… (More)

- Jakob Ablinger, Johannes Blümlein
- ArXiv
- 2013

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… (More)

- Jakob Ablinger, Carsten Schneider
- ArXiv
- 2015

- J Ablinger
- 2013

A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as… (More)