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Computer Algebra and Hypergeometric Structures for Feynman Integrals
Johannes Bluemlein, Marco Saragnese, Carsten Schneider
We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations.…
Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers
J Ablinger, J Blümlein, C Schneider
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, sp…
Harmonic Sums, Polylogarithms, Special Numbers, and their Generalizations
Jakob Ablinger, Johannes Blümlein
In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation…
Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams
J. Ablinger, J. Blümlein, S. Klein +1
By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums…
Structural Relations of Harmonic Sums and Mellin Transforms at Weight w=6
Johannes Blümlein
We derive the structural relations between nested harmonic sums and the corresponding Mellin transforms of Nielsen integrals and harmonic polylogarithms at weight {\sf w = 6}. They…