{"paper":{"title":"Mehler's formulas for the univariate complex Hermite polynomials and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Allal Ghanmi","submitted_at":"2017-07-21T16:41:21Z","abstract_excerpt":"We give two widest Mehler's formulas for the univariate complex Hermite polynomials $H_{m,n}^\\nu$, by performing double summations involving the products $u^m H_{m,n}^\\nu (z,\\overline{z}) \\overline{H_{m,n}^\\nu (w,\\overline{w})}$ and $u^m v^n H_{m,n}^\\nu (z,\\overline{z}) \\overline{H_{m,n}^{\\nu'} (w,\\overline{w})}$. They can be seen as the complex analogues of the classical Mehler's formula for the real Hermite polynomials. The proof of the first one is based on a generating function giving rise to the reproducing kernel of the generalized Bargmann space of level $m$. The second Mehler's formula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06969","kind":"arxiv","version":1},"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"}