{"paper":{"title":"On the Sums of Inverse Even Powers of Zeros of Regular Bessel Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jorge L. deLyra","submitted_at":"2013-05-01T17:23:14Z","abstract_excerpt":"We provide a new, simple general proof of the formulas giving the infinite sums $\\sigma(p,\\nu)$ of the inverse even powers $2p$ of the zeros $\\xi_{\\nu k}$ of the regular Bessel functions $J_{\\nu}(\\xi)$, as functions of $\\nu$. We also give and prove a general formula for certain linear combinations of these sums, which can be used to derive the formulas for $\\sigma(p,\\nu)$ by purely linear-algebraic means, in principle for arbitrarily large powers. We prove that these sums are always given by a ratio of two polynomials on $\\nu$, with integer coefficients. We complete the set of known formulas f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0228","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"}