{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WVPD5BWCATY66IZVVGU4FLTHU4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7641a77034f39dcb19b9adbd968d015a3f2e11312f6d78634c3e4c1966813dcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-14T03:01:59Z","title_canon_sha256":"dfdef7e61d6d7a40a02888979203d6331562c1311e36d79de6e3e2b13992ec2a"},"schema_version":"1.0","source":{"id":"1310.5592","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5592","created_at":"2026-05-18T01:25:16Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5592v3","created_at":"2026-05-18T01:25:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5592","created_at":"2026-05-18T01:25:16Z"},{"alias_kind":"pith_short_12","alias_value":"WVPD5BWCATY6","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WVPD5BWCATY66IZV","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WVPD5BWC","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:159ec948cc0888260d49397adf9ffe3fb81c376125b98c0a86a09d94e9c085b9","target":"graph","created_at":"2026-05-18T01:25:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper proposes a global Pad\\'{e} approximation of the generalized Mittag-Leffler function $E_{\\alpha,\\beta}(-x)$ with $x\\in[0,+\\infty)$. This uniform approximation can account for both the Taylor series for small arguments and asymptotic series for large arguments. Based on the complete monotonicity of the function $E_{\\alpha,\\beta}(-x)$, we work out the global Pad\\'{e} approximation [1/2] for the particular cases $\\{0<\\alpha<1, \\beta>\\alpha\\}$, $\\{0<\\alpha=\\beta<1\\}$, and $\\{\\alpha=1, \\beta>1\\}$, respectively. Moreover, these approximations are inverted to yield a global Pad\\'{e} approxi","authors_text":"Caibin Zeng, YangQuan Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-14T03:01:59Z","title":"Global Pad\\'e approximations of the generalized Mittag-Leffler function and its inverse"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5592","kind":"arxiv","version":3},"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:c569014750162ae84f446e2ffba9b3d9104a382d079c7eaaebb17976ff95f184","target":"record","created_at":"2026-05-18T01:25:16Z","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":"7641a77034f39dcb19b9adbd968d015a3f2e11312f6d78634c3e4c1966813dcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-14T03:01:59Z","title_canon_sha256":"dfdef7e61d6d7a40a02888979203d6331562c1311e36d79de6e3e2b13992ec2a"},"schema_version":"1.0","source":{"id":"1310.5592","kind":"arxiv","version":3}},"canonical_sha256":"b55e3e86c204f1ef2335a9a9c2ae67a72a20c8380353fb5d17ce9165f477ad57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b55e3e86c204f1ef2335a9a9c2ae67a72a20c8380353fb5d17ce9165f477ad57","first_computed_at":"2026-05-18T01:25:16.403879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:16.403879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fnzmNSJXCPoCGNr8lFiAsBJqYxsm3zHBvshPBdkyyWC9TXAAZx9MOQwpsIWTKIadn2DjQ3jqgBo+W9aCbs1qAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:16.404347Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5592","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c569014750162ae84f446e2ffba9b3d9104a382d079c7eaaebb17976ff95f184","sha256:159ec948cc0888260d49397adf9ffe3fb81c376125b98c0a86a09d94e9c085b9"],"state_sha256":"0093b5a991529be82cf94887138f928b48ea7025dd88b1064cc17e32673b7a65"}