{"paper":{"title":"Square Series Generating Function Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maxie D. Schmidt","submitted_at":"2016-09-09T14:09:59Z","abstract_excerpt":"We construct new integral representations for transformations of the ordinary generating function for a sequence, $\\langle f_n \\rangle$, into the form of a generating function that enumerates the corresponding \"square series\" generating function for the sequence, $\\langle q^{n^2} f_n \\rangle$, at an initially fixed non-zero $q \\in \\mathbb{C}$. The new results proved in the article are given by integral-based transformations of ordinary generating function series expanded in terms of the Stirling numbers of the second kind. We then employ known integral representations for the gamma and double "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02803","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"}