{"paper":{"title":"Symbolic integration of a product of two spherical bessel functions with an additional exponential and polynomial factor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-th"],"primary_cat":"physics.comp-ph","authors_text":"B. Gebremariam, S. K. Bogner, T. Duguet","submitted_at":"2009-10-27T19:56:08Z","abstract_excerpt":"We present a mathematica package that performs the symbolic calculation of integrals of the form \\int^{\\infty}_0 e^{-x/u} x^n j_{\\nu} (x) j_{\\mu} (x) dx where $j_{\\nu} (x)$ and $j_{\\mu} (x)$ denote spherical Bessel functions of integer orders, with $\\nu \\ge 0$ and $\\mu \\ge 0$. With the real parameter $u>0$ and the integer $n$, convergence of the integral requires that $n+\\nu +\\mu \\ge 0$. The package provides analytical result for the integral in its most simplified form. The novel symbolic method employed enables the calculation of a large number of integrals of the above form in a fraction of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4993","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"}