{"paper":{"title":"Complete Monotonicity of classical theta functions and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"A. Raouf Chouikha","submitted_at":"2014-09-04T17:23:52Z","abstract_excerpt":"We produce trigonometric expansions for Jacobi theta functions\\\\ $\\theta_j(u,\\tau), j=1,2,3,4$\\ where $\\tau=i\\pi t, t > 0$. This permits us to prove that\\ $\\log \\frac{\\theta_j(u, t)}{\\theta_j(0, t)}, j=2,3,4$ and $\\log \\frac{\\theta_1(u, t)}{\\pi \\theta'_1(0, t)}$ as well as $\\frac{\\frac{\\delta\\theta_j}{\\delta u}}{\\theta_j}$ as functions of $t$ are completely monotonic. We also interested in the quotients $S_j(u,v,t) = \\frac{\\theta_j(u/2,i\\pi t)}{\\theta_j(u/2,i\\pi t)}$. For fixed $u,v$ such that $0\\leq u < v < 1$ we prove that the functions $\\frac{(\\frac{\\delta}{\\delta t}S_j)}{S_j}$ for $j=1,4$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1498","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":""},"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"}