{"paper":{"title":"The evaluation of infinite sums of products of Bessel functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"R B Paris","submitted_at":"2018-03-07T16:49:37Z","abstract_excerpt":"We examine convergent representations for the sum of Bessel functions \\[\\sum_{n=1}^\\infty \\frac{J_\\mu(na) J_\\nu(nb)}{n^{\\alpha}}\\] for $\\mu$, $\\nu\\geq0$ and positive values of $a$ and $b$. Such representations enable easy computation of the series in the limit $a, b\\to0+$. Particular attention is given to logarithmic cases that occur both when $a=b$ and $a\\neq b$ for certain values of $\\alpha$, $\\mu$ and $\\nu$. The series when the first Bessel function is replaced by the modified Bessel function $K_\\mu(na)$ is also investigated, as well as the series with two modified Bessel functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02757","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"}