{"paper":{"title":"An Invertible Family of Hurwitz--Lerch Type Functions Associated with $k$-Augmented Centered Triangular Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Francis Jay R. Romagos, Mark Ivan P. Arcillas, Marlon S. Frias, Noel B. Lacpao, Rey Carl P. Tiu, Rushel S. Acope","submitted_at":"2026-07-29T02:34:23Z","abstract_excerpt":"This paper defines a family of Hurwitz--Lerch type functions whose\n  coefficients are the \\(k\\)-augmented centered triangular numbers. For this\n  family, we obtain the convergence conditions, a reduction formula, and an\n  Euler-operator form. A Vandermonde-based inversion formula is derived for a\n  class of polynomially weighted Hurwitz--Lerch functions. The family considered\n  here is the quadratic case with geometric factors \\(1\\), \\(2\\), and \\(4\\).\n  The resulting formulas show that three consecutive functions recover the\n  classical Hurwitz--Lerch transcendent and its first two Euler deriv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26403","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/2607.26403/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"}