{"paper":{"title":"Explicit evaluation of the $q$-Stokes matrices for certain confluent hypergeometric $q$-difference equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jinghong Lin, Xiaomeng Xu, Yiming Ma","submitted_at":"2024-12-03T08:56:07Z","abstract_excerpt":"We prove a connection formula for the basic hypergeomtric function ${}_n\\varphi_{n-1}\\left(\n  a_1,...,a_{n-1},0;\n  b_1,...,b_{n-1}\n  ; q, z\\right)$ by using the $q$-Borel resummation. As an application, we compute $q$-Stokes matrices of a special confluent hypergeometric $q$-difference system with an irregular singularity. We show that by letting $q\\rightarrow 1$, the $q$-Stokes matrices recover the known expressions of the Stokes matrices of the corresponding confluent hypergeometric differential system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.02281","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.02281/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}