225 citations · 3.5k across the 94 of their papers we have counts for
9 papers · 1 filter
The -extension of iterated integrals and nested sums in quantum field theory
J. Blümlein, A. M. Gavrilik, O. Mykhailiv +1
Analytic calculations of zero- and single-scale quantities in perturbative quantum field theory result into special numbers and functions, the first of which have been revealed dur…
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.…
Hypergeometric Structures in Feynman Integrals
J. Blümlein, M. Saragnese, C. Schneider
Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integra…
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…
Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
Jakob Ablinger, Johannes Blümlein, Carsten Schneider
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 s…
Evaluation of Multi-Sums for Large Scale Problems
J. Blümlein, A. Hasselhuhn, C. Schneider
A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t.\ the dimension parameter $\ep$ can be transformed to multi-sums over hype…