{"paper":{"title":"A note on the modified q-Genocchi numbers and polynomials with weight (\\alpha,\\beta) and their interpolation function at negative integers","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Feng Qi, Hassan Jolany, Mehmet A\\c{c}ikg\\\"oz, Serkan Araci","submitted_at":"2011-12-26T23:52:29Z","abstract_excerpt":"The purpose of this paper concerns to establish modified q-Genocchi numbers and polynomials with weight ({\\alpha},{\\beta}). In this paper we investigate special generalized q-Genocchi polynomials and we apply the method of generating function, which are exploited to derive further classes of q-Genocchi polynomials and develop q-Genocchi numbers and polynomials. By using the Laplace-Mellin transformation integral, we define q-Zeta function with weight ({\\alpha},{\\beta}) and by presenting a link between q-Zeta function with weight ({\\alpha},{\\beta}) and q-Genocchi numbers with weight ({\\alpha},{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5902","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"}