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Using the recently discovered (see Arras et al. \\cite{a-a-p-s-stein}) stein operator $\\RR_\\infty$ associated to $F_\\infty$, we introduce a new class of polynomials $$\\PP_\\infty:= \\{ P_n = \\RR^n_\\infty \\textbf{1} \\, : \\, n \\ge 1 \\}.$$ We analysis in details the case where $F_\\infty$ is distributed as the normal product distribution $N_1 \\ti"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.06671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-19T15:35:47Z","cross_cats_sorted":[],"title_canon_sha256":"8e70fec9a582848378be465ecae554411522b33616bc4cf0547de8bf8d2f98e1","abstract_canon_sha256":"09a57061b6c9790b9cfa20ceb8faf4d90f0ca4acbb1711e9a029dd1d32167513"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:02.602672Z","signature_b64":"sg6qW8gCvp/JeWty9eXKox11MrpJQ/e9sSn/ssTzNvNbh/7ay5VsCSVmivhJl4L7mQ7NH/Yb3Hv87Tf6ku3XAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e17e3ac9293b362723a596b65a7409b865c86b3f6b49ebd5a47c6a00b859fe1","last_reissued_at":"2026-05-18T00:23:02.602120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:02.602120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a new Sheffer class of polynomials related to normal product distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dario Gasbarra, Ehsan Azmoodeh","submitted_at":"2018-02-19T15:35:47Z","abstract_excerpt":"Consider a generic random element $F_\\infty= \\sum_{\\text{finite}} \\lambda_k (N^2_k -1)$ in the second Wiener chaos with a finite number of non-zero coefficients in the spectral representation where $(N_k)_{k \\ge 1}$ is a sequence of i.i.d $\\mathscr{N}(0,1)$. 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