{"paper":{"title":"A toolbox to solve coupled systems of differential and difference equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","hep-th","math-ph","math.MP"],"primary_cat":"cs.SC","authors_text":"Abilio De Freitas, Carsten Schneider, Jakob Ablinger, Johannes Bluemlein","submitted_at":"2016-01-08T12:34:28Z","abstract_excerpt":"We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\\it not} request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter $\\ep$ (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t.\\ $\\ep$ and we try to compute the first terms in cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01856","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}