{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QYOPH2HXCL47MKK6PWHF4PP3V6","short_pith_number":"pith:QYOPH2HX","schema_version":"1.0","canonical_sha256":"861cf3e8f712f9f6295e7d8e5e3dfbaf8dfee0bb6302d7b0ead39ad2b57fa1fb","source":{"kind":"arxiv","id":"1605.08904","version":1},"attestation_state":"computed","paper":{"title":"Error functions, Mordell integrals and an integral analogue of partial theta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Zaharescu, Arindam Roy, Atul Dixit","submitted_at":"2016-05-28T15:43:57Z","abstract_excerpt":"A new transformation involving the error function $\\textup{erf}(z)$, the imaginary error function $\\textup{erfi}(z)$, and an integral analogue of a partial theta function is given along with its character analogues. Another complementary error function transformation is also obtained which when combined with the first explains a transformation in Ramanujan's Lost Notebook termed by Berndt and Xu as the one for an integral analogue of theta functions. These transformations are used to obtain a variety of exact and approximate evaluations of some non-elementary integrals involving hypergeometric"},"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":"1605.08904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-28T15:43:57Z","cross_cats_sorted":[],"title_canon_sha256":"8a2eab20058ef4f8da6ec9ec6f959ddf12b310e53cf95ecd282289e39c946481","abstract_canon_sha256":"eede496516f0e82e8d2353a4c7f9ccbf808e9b2915cb8253a398dc5cb42eccaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:22.680641Z","signature_b64":"Bzu/7QppTTWWiz9Z1+gJlKvHcwH7u17sU8ZqHiWvqlv+ykLk2D07axV+g2NcKx5b5g5a2DG2eXq5Ko+zmRkUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"861cf3e8f712f9f6295e7d8e5e3dfbaf8dfee0bb6302d7b0ead39ad2b57fa1fb","last_reissued_at":"2026-05-18T01:13:22.680083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:22.680083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Error functions, Mordell integrals and an integral analogue of partial theta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Zaharescu, Arindam Roy, Atul Dixit","submitted_at":"2016-05-28T15:43:57Z","abstract_excerpt":"A new transformation involving the error function $\\textup{erf}(z)$, the imaginary error function $\\textup{erfi}(z)$, and an integral analogue of a partial theta function is given along with its character analogues. Another complementary error function transformation is also obtained which when combined with the first explains a transformation in Ramanujan's Lost Notebook termed by Berndt and Xu as the one for an integral analogue of theta functions. These transformations are used to obtain a variety of exact and approximate evaluations of some non-elementary integrals involving hypergeometric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08904","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":"1605.08904","created_at":"2026-05-18T01:13:22.680169+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.08904v1","created_at":"2026-05-18T01:13:22.680169+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08904","created_at":"2026-05-18T01:13:22.680169+00:00"},{"alias_kind":"pith_short_12","alias_value":"QYOPH2HXCL47","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"QYOPH2HXCL47MKK6","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"QYOPH2HX","created_at":"2026-05-18T12:30:41.710351+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/QYOPH2HXCL47MKK6PWHF4PP3V6","json":"https://pith.science/pith/QYOPH2HXCL47MKK6PWHF4PP3V6.json","graph_json":"https://pith.science/api/pith-number/QYOPH2HXCL47MKK6PWHF4PP3V6/graph.json","events_json":"https://pith.science/api/pith-number/QYOPH2HXCL47MKK6PWHF4PP3V6/events.json","paper":"https://pith.science/paper/QYOPH2HX"},"agent_actions":{"view_html":"https://pith.science/pith/QYOPH2HXCL47MKK6PWHF4PP3V6","download_json":"https://pith.science/pith/QYOPH2HXCL47MKK6PWHF4PP3V6.json","view_paper":"https://pith.science/paper/QYOPH2HX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.08904&json=true","fetch_graph":"https://pith.science/api/pith-number/QYOPH2HXCL47MKK6PWHF4PP3V6/graph.json","fetch_events":"https://pith.science/api/pith-number/QYOPH2HXCL47MKK6PWHF4PP3V6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QYOPH2HXCL47MKK6PWHF4PP3V6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QYOPH2HXCL47MKK6PWHF4PP3V6/action/storage_attestation","attest_author":"https://pith.science/pith/QYOPH2HXCL47MKK6PWHF4PP3V6/action/author_attestation","sign_citation":"https://pith.science/pith/QYOPH2HXCL47MKK6PWHF4PP3V6/action/citation_signature","submit_replication":"https://pith.science/pith/QYOPH2HXCL47MKK6PWHF4PP3V6/action/replication_record"}},"created_at":"2026-05-18T01:13:22.680169+00:00","updated_at":"2026-05-18T01:13:22.680169+00:00"}