{"paper":{"title":"Complete systems of recursive integrals and Taylor series for solutions of Sturm-Liouville equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Samy Morelos, S\\'ebastien Tremblay, Vladislav V. Kravchenko","submitted_at":"2011-03-27T16:55:12Z","abstract_excerpt":"Consider an arbitrary complex-valued, twice continuously differentiable, nonvanishing function $\\phi$ defined on a finite segment $[a,b]\\subset \\mathbb{R}$. Let us introduce an infinite system of functions constructed in the following way. Each subsequent function is a primitive of the preceding one multiplied or divided by $\\phi$ alternately. The obtained system of functions is a generalization of the system of powers ${(x-x_{0}%)^{k}}_{k=0}^{\\infty}$. We study its completeness as well as the completeness of its subsets in different functional spaces. This system of recursive integrals result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5233","kind":"arxiv","version":3},"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"}