{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5IPBOI3K642OVEJPISYOAU25UX","short_pith_number":"pith:5IPBOI3K","schema_version":"1.0","canonical_sha256":"ea1e17236af734ea912f44b0e0535da5d3f209f18e0c87d0b134bb793dab8d34","source":{"kind":"arxiv","id":"1510.00406","version":1},"attestation_state":"computed","paper":{"title":"Notes on the q-Analogues of the Natural Transforms and Some Further Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Kilicman, S. K. Q. Al-Omari","submitted_at":"2015-09-28T03:59:33Z","abstract_excerpt":"As an extension to the Laplace and Sumudu transforms the classical Natural transform was proposed to solve certain fluid flow problems. In this paper, we investigate q-analogues of the q-Natural transform of some special functions. We derive the q-analogues of the q-integral transform and further apply to some general special functions such as : the exponential functions, the q-trigonometric functions, the q-hyperbolic functions and the Heaviside Function. Some further results involving convolutions and differentiations are also obtained."},"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":"1510.00406","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-28T03:59:33Z","cross_cats_sorted":[],"title_canon_sha256":"96302fcdd71bdf1afe3c801e190d802ae838649ecc559b6170860f309c74fbd7","abstract_canon_sha256":"f7414a9c4feb04a78f2e76c2e32e419f61ea057fb45c7dfebf6a3a209c81a753"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:13.175088Z","signature_b64":"F0sxIbuR+OCBqlg0aAO3GyRzTv/pw15LjXjRjTU+pQcQdptz4mza+1KLq2FtUicmHSEI4bDZCEXvzbbWDGOiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea1e17236af734ea912f44b0e0535da5d3f209f18e0c87d0b134bb793dab8d34","last_reissued_at":"2026-05-18T01:31:13.174425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:13.174425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Notes on the q-Analogues of the Natural Transforms and Some Further Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Kilicman, S. K. Q. Al-Omari","submitted_at":"2015-09-28T03:59:33Z","abstract_excerpt":"As an extension to the Laplace and Sumudu transforms the classical Natural transform was proposed to solve certain fluid flow problems. In this paper, we investigate q-analogues of the q-Natural transform of some special functions. We derive the q-analogues of the q-integral transform and further apply to some general special functions such as : the exponential functions, the q-trigonometric functions, the q-hyperbolic functions and the Heaviside Function. Some further results involving convolutions and differentiations are also obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00406","kind":"arxiv","version":1},"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":"1510.00406","created_at":"2026-05-18T01:31:13.174526+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.00406v1","created_at":"2026-05-18T01:31:13.174526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00406","created_at":"2026-05-18T01:31:13.174526+00:00"},{"alias_kind":"pith_short_12","alias_value":"5IPBOI3K642O","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5IPBOI3K642OVEJP","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5IPBOI3K","created_at":"2026-05-18T12:29:05.191682+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/5IPBOI3K642OVEJPISYOAU25UX","json":"https://pith.science/pith/5IPBOI3K642OVEJPISYOAU25UX.json","graph_json":"https://pith.science/api/pith-number/5IPBOI3K642OVEJPISYOAU25UX/graph.json","events_json":"https://pith.science/api/pith-number/5IPBOI3K642OVEJPISYOAU25UX/events.json","paper":"https://pith.science/paper/5IPBOI3K"},"agent_actions":{"view_html":"https://pith.science/pith/5IPBOI3K642OVEJPISYOAU25UX","download_json":"https://pith.science/pith/5IPBOI3K642OVEJPISYOAU25UX.json","view_paper":"https://pith.science/paper/5IPBOI3K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.00406&json=true","fetch_graph":"https://pith.science/api/pith-number/5IPBOI3K642OVEJPISYOAU25UX/graph.json","fetch_events":"https://pith.science/api/pith-number/5IPBOI3K642OVEJPISYOAU25UX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5IPBOI3K642OVEJPISYOAU25UX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5IPBOI3K642OVEJPISYOAU25UX/action/storage_attestation","attest_author":"https://pith.science/pith/5IPBOI3K642OVEJPISYOAU25UX/action/author_attestation","sign_citation":"https://pith.science/pith/5IPBOI3K642OVEJPISYOAU25UX/action/citation_signature","submit_replication":"https://pith.science/pith/5IPBOI3K642OVEJPISYOAU25UX/action/replication_record"}},"created_at":"2026-05-18T01:31:13.174526+00:00","updated_at":"2026-05-18T01:31:13.174526+00:00"}