{"paper":{"title":"An Analytical Evaluation For The Integral Of Two Spherical Bessel Functions With An Additional Exponential And Polynomial Factor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nucl-th"],"primary_cat":"math-ph","authors_text":"R. Mehrem","submitted_at":"2011-10-27T18:11:46Z","abstract_excerpt":"The integrals $\\threej{\\Llo}{\\Llt}{\\Llth} {0}{0}{0}\\,\\int_0^\\infty \\,r^{\\Llth+1}\\,e^{-\\alpha r}\\,j_\\Llo(k_1r)\\, j_\\Llt(k_2r)\\,dr$ and $\\threej{\\Llo}{\\Llt}{\\Llth} {0}{0}{0}\\,\\int_0^\\infty \\,r^{\\Llth+2}\\,e^{-\\alpha r}\\,j_\\Llo(k_1r)\\, j_\\Llt(k_2r)\\,dr$ are evaluated analytically. The result is a finite sum over the associated Legendre function of the second kind."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6147","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"}