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Numerical results illustrating the accuracy of the resulting expansion are given."},"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":"1810.01134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-02T09:29:21Z","cross_cats_sorted":[],"title_canon_sha256":"8a341e90093b2149bc1f06691bd63ad8cc3c8bc3e37c4a554ecc3deed6f1abe0","abstract_canon_sha256":"7b2ff988d271df25e4c70dae683e33a3b0fb5e8f6883a8666c3ad77a1dd1f5ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:18.712263Z","signature_b64":"OniH/zVwipU8jNO646sG4BKB7ZNGF1uvkc6QfJDswepg9gOI+CBOYxNXyQvY8Uv+tR+VkWD0CxQ8Ygue/W7dBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fd00a77e56c379493374863976ffd07f49e90bff6f82f6c8836f48735e53a89","last_reissued_at":"2026-05-18T00:04:18.711603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:18.711603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of a ${}_3F_2$ hypergeometric function with four large parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"R B Paris","submitted_at":"2018-10-02T09:29:21Z","abstract_excerpt":"We consider the asymptotic behaviour of the generalised hypergeometric function \\[{}_3F_2\\bl(\\!\\!\\begin{array}{c} 1, (1+t)k/2, (1+t)k/2+1/2\\\\tk+1, k+1\\end{array}\\!\\!; x\\br),\\qquad 0<x,t\\leq 1\\] as the parameter $k\\to+\\infty$. 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