{"paper":{"title":"Explicit calculation of multi-fold contour integrals of certain ratios of Euler gamma functions. Part 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Bernd A. Kniehl, Eduardo A. Notte-Cuello, Igor Kondrashuk, Ivan Gonzalez, Ivan Parra-Ferrada, Marko A. Rojas-Medar","submitted_at":"2016-08-14T22:35:15Z","abstract_excerpt":"In this paper we proceed to study properties of Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions. In our previous papers [Nuclear Physics B 870 (2013) 243], [Nuclear Physics B 876 (2013) 322] we showed that multi-fold Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions may be reduced to two-fold MB transforms and that the higher-order UD functions were obtained in terms of a differential operator by applying it to a slightly modified first UD function. The result is valid in $d=4$ dimensions and its analog in $d=4-2\\varepsilon$ dimensions exits too [Theoretic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04148","kind":"arxiv","version":2},"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"}