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We investigate the following problem: For which ratio $N/n$ and which functions, do we have pointwise convergence of the least square operator ${LS}_n^N:\\mathcal{C}\\left[-1,1\\right]\\rightarrow\\mathcal{P}_n$? To solve this problem we investigate the relation between the Jacobi polynomials $P_k^{\\alpha,\\beta}$ and the Hahn polynomials $Q_k\\left(\\cdot;\\alpha,\\beta,N\\right)$. Thereby we describe the least square operator ${LS}_n^N$ by the expansion of a function by Hahn polynomials."},"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":"1610.06748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-21T12:00:11Z","cross_cats_sorted":[],"title_canon_sha256":"8300cb6d5580a1e850524304cfbe79b7e84eb2f6504e4f700f55fcac5c5c6b6f","abstract_canon_sha256":"f40fada6ed7550d34354e74c7bdeaf8e248fbbed7409b78e6773b571e980c333"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:36.823587Z","signature_b64":"TBgUvsr1BbVhrNi8o5D+6MDbSnS8CgdabvWA7/S//iTbVPDFNFCQxDD57aau8rsVNx/JKeirsQeDkNJ3CQkmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b00a63d0dbf7fc69bb4c9912725f7a36ca7dd6e907200b89fb6edd2b7cc652d","last_reissued_at":"2026-05-18T01:01:36.823054Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:36.823054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Hahn polynomial expansion of a continuous function of bounded variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Philipp \\\"Offner, Ren\\'e Goertz","submitted_at":"2016-10-21T12:00:11Z","abstract_excerpt":"We consider the well-known method of least squares on an equidistant grid with $N+1$ nodes on the interval $[-1,1]$. We investigate the following problem: For which ratio $N/n$ and which functions, do we have pointwise convergence of the least square operator ${LS}_n^N:\\mathcal{C}\\left[-1,1\\right]\\rightarrow\\mathcal{P}_n$? To solve this problem we investigate the relation between the Jacobi polynomials $P_k^{\\alpha,\\beta}$ and the Hahn polynomials $Q_k\\left(\\cdot;\\alpha,\\beta,N\\right)$. 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