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For fixed k \\geq 0 and appropriate values of the spectral parameter {\\lambda}, the equation \\ell[y]={\\lambda}y has, as in the classical case, a sequence of (Jacobi) polynomial solutions {P_{n}^{(-1,-1)}}_{n=0}^{\\infty}. These Jacobi polynomial solutions of degree \\geq 2 form a complete orthogonal set in th","authors_text":"Andrea Bruder, Lance Littlejohn","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-23T02:37:41Z","title":"Classical and Sobolev Orthogonality of the Nonclassical Jacobi Polynomials with Parameters {\\alpha}={\\beta}=-1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5085","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:349c68538c04e2c929e7ee1c3da9d5457139d4d1f3f7c6aba1c41afb9d44512b","target":"record","created_at":"2026-05-18T03:55:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6242ad3f4d22185d2a5a12bed9a3b2845811ea4dec87ee9727e408bd6765c068","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-23T02:37:41Z","title_canon_sha256":"458d9cde2460db07004be560025923e93bd66be39e1b030b787c10e7383f364e"},"schema_version":"1.0","source":{"id":"1205.5085","kind":"arxiv","version":1}},"canonical_sha256":"411a84182d2b16827a507b3a72ec5965ad0c264f46fceb9c7db46b5a9109aa68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"411a84182d2b16827a507b3a72ec5965ad0c264f46fceb9c7db46b5a9109aa68","first_computed_at":"2026-05-18T03:55:02.247086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:02.247086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rexbkeIfy3W86nMuIiYvTsyyf8oaiKI40Q5saLhrxbX+Xik8CX8b7PE5dr8utIuQGFUCAmop8GSPoYIsH5q+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:02.247607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:349c68538c04e2c929e7ee1c3da9d5457139d4d1f3f7c6aba1c41afb9d44512b","sha256:d7faa7eeb89352a707dae5f2f9b05f5735a5af5fe43e463e201984aa43f7dd8d"],"state_sha256":"d35563e11be5390dc625165e3837fd6a0a8344c037913ad5e3ce1b182388d0c1"}