{"paper":{"title":"Complex Hermite functions as Fourier-Wigner transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Allal Ghanmi, Amal El Hamyani, Arij Benkhadra, Fatima Agorram","submitted_at":"2015-06-23T16:40:22Z","abstract_excerpt":"We prove that the complex Hermite polynomials H_{m,n} on the complex plane $\\mathbb{C}$ can be realized as the Fourier-Wigner transform $\\mathcal{V}$ of the well-known real Hermite functions $h_n$ on real line $\\mathbb{R}$. This reduces considerably the Wong's proof giving the explicit expression of $\\mathcal{V}(h_m,h_n)$ in terms of the Laguerre polynomials. Moreover, we derive a new generating function for the H_{m,n} as well as some new integral identities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07084","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"}