{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NFJFNXP3WWGN5CQDZ6MQP4AS5T","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":"92554953461d5bc09411f3a542d9f1987a0afea451c4216530a1fd77f52fb7b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-19T13:17:22Z","title_canon_sha256":"6d287f41d90be9ac8ee88ead1381751356af1b45169cf4162b5d73eb452f4574"},"schema_version":"1.0","source":{"id":"1405.4712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4712","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4712v1","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4712","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"pith_short_12","alias_value":"NFJFNXP3WWGN","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NFJFNXP3WWGN5CQD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NFJFNXP3","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:cf7b25fc1ee4665a9cebd5a91b626a6d24aa8b54d21c08adf6d451d87467baaf","target":"graph","created_at":"2026-05-18T00:40:24Z","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":"We deduce some new functional inequalities, like Tur\\'an type inequalities, Redheffer type inequalities, and a Mittag-Leffler expansion for a special combination of modified Bessel functions of the first kind, called modified Dini functions. Moreover, we show the complete monotonicity of a quotient of modified Dini functions by introducing a new continuous infinitely divisible probability distribution. The key tool in our proofs is a recently developed infinite product representation for a special combination of Bessel functions of the first, which was very useful in determining the radius of ","authors_text":"\\'A. Baricz, S. Ponnusamy, S. Singh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-19T13:17:22Z","title":"Modified Dini functions: monotonicity patterns and functional inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4712","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":"sha256:2e7ac4b1c8e755cf09b9f3019ded0c6b77b1e644676d61abfad72ed1bce88293","target":"record","created_at":"2026-05-18T00:40:24Z","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":"92554953461d5bc09411f3a542d9f1987a0afea451c4216530a1fd77f52fb7b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-19T13:17:22Z","title_canon_sha256":"6d287f41d90be9ac8ee88ead1381751356af1b45169cf4162b5d73eb452f4574"},"schema_version":"1.0","source":{"id":"1405.4712","kind":"arxiv","version":1}},"canonical_sha256":"695256ddfbb58cde8a03cf9907f012eccc957605bec136b25ea2c9871f47299e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"695256ddfbb58cde8a03cf9907f012eccc957605bec136b25ea2c9871f47299e","first_computed_at":"2026-05-18T00:40:24.644601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:24.644601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8H9xMtPHajrbw6pcCnVv3KLOY8zhzzWQfpjx6RgaJWJlfWKhOlfsz9KYn8+E3939uNZMQtoQakpGNfFZiBqRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:24.645337Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e7ac4b1c8e755cf09b9f3019ded0c6b77b1e644676d61abfad72ed1bce88293","sha256:cf7b25fc1ee4665a9cebd5a91b626a6d24aa8b54d21c08adf6d451d87467baaf"],"state_sha256":"902b9aa8fb5768968d8ee045f2ccc69ea0336670802e4e8a345b093a89f82d84"}