{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3VZU2TSDELR3T2JDUFIEUF7EOK","short_pith_number":"pith:3VZU2TSD","schema_version":"1.0","canonical_sha256":"dd734d4e4322e3b9e923a1504a17e472ac39a79a5faae50ecd50b098df4a2ed9","source":{"kind":"arxiv","id":"1606.03621","version":3},"attestation_state":"computed","paper":{"title":"On a function involving generalized complete $(p,q)$- elliptic integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Barkat Ali Bhayo, Li Yin","submitted_at":"2016-06-11T20:29:53Z","abstract_excerpt":"Motivated by the work of Alzer and Richards \\cite{ar}, here authors study the monotonicity and convexity properties of the function $$\\Delta_{p,q} (r) = \\frac{{E_{p,q}(r) - \\left( {r'} \\right)^p K_{p,q}(r) }}{{r^p }} - \\frac{{E'_{p,q}(r) - r^p K'_{p,q}(r) }}{{\\left( {r'} \\right)^p }},$$ where $K_{p,q}$ and $E_{p,q}$ denote the complete $(p,q)$- elliptic integrals of the first and the second kind, respectively."},"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":"1606.03621","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-11T20:29:53Z","cross_cats_sorted":[],"title_canon_sha256":"09ffcef96ba845a75c57634358e7fa3f98abb899fd79210556d5876b977d5362","abstract_canon_sha256":"b05a3bbc67bfb40fec7534a1349cfb8ad9638b57bedea38cd818bd99aa78b249"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:33.159637Z","signature_b64":"mclZOJIdC0B0RZAtoK1q1mcpgsJ1g6Jfs/zOQ3K5QwhARanyztZYNnW/VcIz6+xn9cRofdeSf+gQ8aWDkZfjCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd734d4e4322e3b9e923a1504a17e472ac39a79a5faae50ecd50b098df4a2ed9","last_reissued_at":"2026-05-17T23:57:33.159186Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:33.159186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a function involving generalized complete $(p,q)$- elliptic integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Barkat Ali Bhayo, Li Yin","submitted_at":"2016-06-11T20:29:53Z","abstract_excerpt":"Motivated by the work of Alzer and Richards \\cite{ar}, here authors study the monotonicity and convexity properties of the function $$\\Delta_{p,q} (r) = \\frac{{E_{p,q}(r) - \\left( {r'} \\right)^p K_{p,q}(r) }}{{r^p }} - \\frac{{E'_{p,q}(r) - r^p K'_{p,q}(r) }}{{\\left( {r'} \\right)^p }},$$ where $K_{p,q}$ and $E_{p,q}$ denote the complete $(p,q)$- elliptic integrals of the first and the second kind, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03621","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.03621","created_at":"2026-05-17T23:57:33.159246+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.03621v3","created_at":"2026-05-17T23:57:33.159246+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03621","created_at":"2026-05-17T23:57:33.159246+00:00"},{"alias_kind":"pith_short_12","alias_value":"3VZU2TSDELR3","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"3VZU2TSDELR3T2JD","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"3VZU2TSD","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3VZU2TSDELR3T2JDUFIEUF7EOK","json":"https://pith.science/pith/3VZU2TSDELR3T2JDUFIEUF7EOK.json","graph_json":"https://pith.science/api/pith-number/3VZU2TSDELR3T2JDUFIEUF7EOK/graph.json","events_json":"https://pith.science/api/pith-number/3VZU2TSDELR3T2JDUFIEUF7EOK/events.json","paper":"https://pith.science/paper/3VZU2TSD"},"agent_actions":{"view_html":"https://pith.science/pith/3VZU2TSDELR3T2JDUFIEUF7EOK","download_json":"https://pith.science/pith/3VZU2TSDELR3T2JDUFIEUF7EOK.json","view_paper":"https://pith.science/paper/3VZU2TSD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.03621&json=true","fetch_graph":"https://pith.science/api/pith-number/3VZU2TSDELR3T2JDUFIEUF7EOK/graph.json","fetch_events":"https://pith.science/api/pith-number/3VZU2TSDELR3T2JDUFIEUF7EOK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3VZU2TSDELR3T2JDUFIEUF7EOK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3VZU2TSDELR3T2JDUFIEUF7EOK/action/storage_attestation","attest_author":"https://pith.science/pith/3VZU2TSDELR3T2JDUFIEUF7EOK/action/author_attestation","sign_citation":"https://pith.science/pith/3VZU2TSDELR3T2JDUFIEUF7EOK/action/citation_signature","submit_replication":"https://pith.science/pith/3VZU2TSDELR3T2JDUFIEUF7EOK/action/replication_record"}},"created_at":"2026-05-17T23:57:33.159246+00:00","updated_at":"2026-05-17T23:57:33.159246+00:00"}