{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:I7QOK6FQATBK2W5CYB6DSVKVIM","short_pith_number":"pith:I7QOK6FQ","schema_version":"1.0","canonical_sha256":"47e0e578b004c2ad5ba2c07c3955554314f324e33c4c43e9deb5bd7c457b640a","source":{"kind":"arxiv","id":"1303.3978","version":1},"attestation_state":"computed","paper":{"title":"Erdelyi-Kober Fractional Integral Operators from a Statistical Perspective -I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A.M. Mathai, H.J. Haubold","submitted_at":"2013-03-16T13:49:15Z","abstract_excerpt":"In this article we examine the densities of a product and a ratio of two real positive scalar random variables $x_1$ and $x_2$, which are statistically independently distributed, and we consider the density of the product $u_1=x_1x_2$ as well as the density of the ratio $u_2={{x_2}\\over{x_1}}$ and show that Kober operator of the second kind is available as the density of $u_1$ and Kober operator of the first kind is available as the density of $u_2$ when $x_1$ has a type-1 beta density and $x_2$ has an arbitrary density. We also give interpretations of Kober operators of the second and first k"},"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":"1303.3978","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-16T13:49:15Z","cross_cats_sorted":[],"title_canon_sha256":"d9bdfdbd4916270fd6664a6fc6b64a12ad71dfd73e15b22a100cbc7525670258","abstract_canon_sha256":"f801934a916827dce3ce6930429c9ae32a7ed28ff560054dab89064d9d435d7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:40.309526Z","signature_b64":"2CX/FGjQsqE0+NE7TXk7DDp3S2/vZOIv9jHI8NwFGfFEMg40zxSG85FG9biLuBafEmrlqSXyEI8LKsIMbVEiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47e0e578b004c2ad5ba2c07c3955554314f324e33c4c43e9deb5bd7c457b640a","last_reissued_at":"2026-05-18T03:30:40.308652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:40.308652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Erdelyi-Kober Fractional Integral Operators from a Statistical Perspective -I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A.M. Mathai, H.J. Haubold","submitted_at":"2013-03-16T13:49:15Z","abstract_excerpt":"In this article we examine the densities of a product and a ratio of two real positive scalar random variables $x_1$ and $x_2$, which are statistically independently distributed, and we consider the density of the product $u_1=x_1x_2$ as well as the density of the ratio $u_2={{x_2}\\over{x_1}}$ and show that Kober operator of the second kind is available as the density of $u_1$ and Kober operator of the first kind is available as the density of $u_2$ when $x_1$ has a type-1 beta density and $x_2$ has an arbitrary density. We also give interpretations of Kober operators of the second and first k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3978","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":"1303.3978","created_at":"2026-05-18T03:30:40.308794+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.3978v1","created_at":"2026-05-18T03:30:40.308794+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3978","created_at":"2026-05-18T03:30:40.308794+00:00"},{"alias_kind":"pith_short_12","alias_value":"I7QOK6FQATBK","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"I7QOK6FQATBK2W5C","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"I7QOK6FQ","created_at":"2026-05-18T12:27:46.883200+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/I7QOK6FQATBK2W5CYB6DSVKVIM","json":"https://pith.science/pith/I7QOK6FQATBK2W5CYB6DSVKVIM.json","graph_json":"https://pith.science/api/pith-number/I7QOK6FQATBK2W5CYB6DSVKVIM/graph.json","events_json":"https://pith.science/api/pith-number/I7QOK6FQATBK2W5CYB6DSVKVIM/events.json","paper":"https://pith.science/paper/I7QOK6FQ"},"agent_actions":{"view_html":"https://pith.science/pith/I7QOK6FQATBK2W5CYB6DSVKVIM","download_json":"https://pith.science/pith/I7QOK6FQATBK2W5CYB6DSVKVIM.json","view_paper":"https://pith.science/paper/I7QOK6FQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.3978&json=true","fetch_graph":"https://pith.science/api/pith-number/I7QOK6FQATBK2W5CYB6DSVKVIM/graph.json","fetch_events":"https://pith.science/api/pith-number/I7QOK6FQATBK2W5CYB6DSVKVIM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I7QOK6FQATBK2W5CYB6DSVKVIM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I7QOK6FQATBK2W5CYB6DSVKVIM/action/storage_attestation","attest_author":"https://pith.science/pith/I7QOK6FQATBK2W5CYB6DSVKVIM/action/author_attestation","sign_citation":"https://pith.science/pith/I7QOK6FQATBK2W5CYB6DSVKVIM/action/citation_signature","submit_replication":"https://pith.science/pith/I7QOK6FQATBK2W5CYB6DSVKVIM/action/replication_record"}},"created_at":"2026-05-18T03:30:40.308794+00:00","updated_at":"2026-05-18T03:30:40.308794+00:00"}