{"paper":{"title":"Around Poisson--Mehler summation formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Pawe{\\l} J. Szab{\\l}owski","submitted_at":"2011-08-15T15:50:20Z","abstract_excerpt":"We study polynomials in $x$ and $y$ of degree $n+m:\\allowbreak \\{Q_{m,n}(x,y|t,q)\\}_{n,m\\geq 0}$ that appeared recently in the following identity: $\\gamma_{m,n}(x,y|t,q) \\allowbreak =\\allowbreak \\gamma_{0,0}(x,y|t,q) \\allowbreak Q_{m,n}(x,y|t,q) $ where $\\gamma_{m,n}(x,y|t,q) \\allowbreak =\\allowbreak \\sum_{i\\geq 0}\\frac{t^{i}}{[i]_{q}}H_{i+n}(x|q) H_{m+i}(y|q)$, $\\allowbreak $ $\\{H_{n}(x|q)}_{n\\geq -1}$ are the so-called $q-$% Hermite polynomials (qH). In particular we show that the spaces $span\\{Q_{i,n-i}(x,y|t,q) :i=0,...,n\\}_{n\\geq 0}$ are orthogonal with respect to a certain measure (two-d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3024","kind":"arxiv","version":4},"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"}