{"paper":{"title":"The Integral Representation for the Product of Two Parabolic Cylinder Functions $D_\\nu (x) D_\\nu (-x)$ at $Re \\nu <0$ by Means of the Fundamental Solution of a Landau-Type Operator","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"C. Malyshev","submitted_at":"2001-06-17T13:32:57Z","abstract_excerpt":"The fundamental solution (Green's function) of a first order matrix ordinary differential equation arising in a Landau-type problem is calculated by two methods. The coincidence of the two representations results in the integral formula for the product of two parabolic cylinder functions $D_\\nu(x) D_\\nu(-x)$ at $Re \\nu <0$, $x$ is real."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0106142","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"}