{"paper":{"title":"A generalized modified Bessel function and a higher level analogue of the theta transformation formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Aashita Kesarwani, Atul Dixit, Nico M. Temme, Victor H. Moll","submitted_at":"2017-06-16T17:37:14Z","abstract_excerpt":"A new generalization of the modified Bessel function of the second kind $K_{z}(x)$ is studied. Elegant series and integral representations, a differential-difference equation and asymptotic expansions are obtained for it thereby anticipating a rich theory that it may possess. The motivation behind introducing this generalization is to have a function which gives a new pair of functions reciprocal in the Koshliakov kernel $\\cos \\left( {{\\pi z}} \\right){M_{2z}}(4\\sqrt {x} ) - \\sin \\left( {{\\pi z}} \\right){J_{2z}}(4\\sqrt {x} )$ and which subsumes the self-reciprocal pair involving $K_{z}(x)$. Its"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05363","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"}