{"paper":{"title":"Inversion formula with hypergeometric polynomials and its application to an integral equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.PF"],"primary_cat":"math.CA","authors_text":"Alain Simonian, Fabrice Guillemin, Ridha Nasri","submitted_at":"2019-04-16T17:23:32Z","abstract_excerpt":"For any complex parameters $x$ and $\\nu$, we provide a new class of linear inversion formulas $T = A(x,\\nu) \\cdot S \\Leftrightarrow S = B(x,\\nu) \\cdot T$ between sequences $S = (S_n)_{n \\in \\mathbb{N}^*}$ and $T = (T_n)_{n \\in \\mathbb{N}^*}$, where the infinite lower-triangular matrix $A(x,\\nu)$ and its inverse $B(x,\\nu)$ involve Hypergeometric polynomials $F(\\cdot)$, namely $$\n  \\left\\{\n  \\begin{array}{ll}\n  A_{n,k}(x,\\nu) = \\displaystyle (-1)^k\\binom{n}{k}F(k-n,-n\\nu;-n;x),\n  \\\\\n  B_{n,k}(x,\\nu) = \\displaystyle (-1)^k\\binom{n}{k}F(k-n,k\\nu;k;x)\n  \\end{array} \\right. $$ for $1 \\leqslant k \\le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08283","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"}