{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2KPS37VPCBA2OOHK5Q6HTMZBBU","short_pith_number":"pith:2KPS37VP","canonical_record":{"source":{"id":"1711.03006","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-07T13:28:46Z","cross_cats_sorted":[],"title_canon_sha256":"701ab932dac5f7dbc14fe55510f82e543b15d8ca43ba32d47d6f0e0adb008d9d","abstract_canon_sha256":"e345971483b2dcf7a7c2cf47ce65e65f9e48c172cc3b33783359f8e2b2c5f7e1"},"schema_version":"1.0"},"canonical_sha256":"d29f2dfeaf1041a738eaec3c79b3210d2392181d1f6026794c274c03d981320d","source":{"kind":"arxiv","id":"1711.03006","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03006","created_at":"2026-07-05T01:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03006v2","created_at":"2026-07-05T01:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03006","created_at":"2026-07-05T01:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"2KPS37VPCBA2","created_at":"2026-07-05T01:09:54Z"},{"alias_kind":"pith_short_16","alias_value":"2KPS37VPCBA2OOHK","created_at":"2026-07-05T01:09:54Z"},{"alias_kind":"pith_short_8","alias_value":"2KPS37VP","created_at":"2026-07-05T01:09:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2KPS37VPCBA2OOHK5Q6HTMZBBU","target":"record","payload":{"canonical_record":{"source":{"id":"1711.03006","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-07T13:28:46Z","cross_cats_sorted":[],"title_canon_sha256":"701ab932dac5f7dbc14fe55510f82e543b15d8ca43ba32d47d6f0e0adb008d9d","abstract_canon_sha256":"e345971483b2dcf7a7c2cf47ce65e65f9e48c172cc3b33783359f8e2b2c5f7e1"},"schema_version":"1.0"},"canonical_sha256":"d29f2dfeaf1041a738eaec3c79b3210d2392181d1f6026794c274c03d981320d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:09:54.441700Z","signature_b64":"c6DaLI0R80ss3XD0i3KTg/zvEJtRsYDgvLxIhi8wGTGuLkf5XnhlWKn6xEk6Ou9oCBcOjOHQXZg/6QnTwmy3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d29f2dfeaf1041a738eaec3c79b3210d2392181d1f6026794c274c03d981320d","last_reissued_at":"2026-07-05T01:09:54.441270Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:09:54.441270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.03006","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:09:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RT7hKBHZ4Xb7VOVSqyRY+7y5NEZ1uwt0ASTej+Fqc1140ocQVoOjpoYUwmS+D6dYD1BzANKExXpT9zSmznXbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T13:26:29.119478Z"},"content_sha256":"b8575750477b1393b46a794040816258e11debc5f71439d6b1b988a1ea06db4c","schema_version":"1.0","event_id":"sha256:b8575750477b1393b46a794040816258e11debc5f71439d6b1b988a1ea06db4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2KPS37VPCBA2OOHK5Q6HTMZBBU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The asymptotics of the generalised Bessel function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"R B Paris","submitted_at":"2017-11-07T13:28:46Z","abstract_excerpt":"We demonstrate how the asymptotics for large $|z|$ of the generalised Bessel function \\[{}_0\\Psi_1(z)=\\sum_{n=0}^\\infty\\frac{z^n}{\\Gamma(an+b) n!},\\] where $a>-1$ and $b$ is any number (real or complex), may be obtained by exploiting the well-established asymptotic theory of the generalised Wright function ${}_p\\Psi_q(z)$. A summary of this theory is given and an algorithm for determining the coefficients in the associated exponential expansions is discussed in an appendix. We pay particular attention to the case $a=-1/2$, where the expansion for $z\\to\\pm\\infty$ consists of an exponentially sm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03006","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1711.03006/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:09:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tKYx3iBSk63QBu9xziqwtDOPfHZAbCkkcgCNclIOf2ltzvVVi6qvBSEJJbYg0lDZ1qNu+PP/8aZh5JHm7mR6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T13:26:29.120019Z"},"content_sha256":"f60aaf1a82d6f22c9c5ed5b0a5a738cc81cb32791203b1bcc24860d81cee40fa","schema_version":"1.0","event_id":"sha256:f60aaf1a82d6f22c9c5ed5b0a5a738cc81cb32791203b1bcc24860d81cee40fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2KPS37VPCBA2OOHK5Q6HTMZBBU/bundle.json","state_url":"https://pith.science/pith/2KPS37VPCBA2OOHK5Q6HTMZBBU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2KPS37VPCBA2OOHK5Q6HTMZBBU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-17T13:26:29Z","links":{"resolver":"https://pith.science/pith/2KPS37VPCBA2OOHK5Q6HTMZBBU","bundle":"https://pith.science/pith/2KPS37VPCBA2OOHK5Q6HTMZBBU/bundle.json","state":"https://pith.science/pith/2KPS37VPCBA2OOHK5Q6HTMZBBU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2KPS37VPCBA2OOHK5Q6HTMZBBU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2KPS37VPCBA2OOHK5Q6HTMZBBU","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":"e345971483b2dcf7a7c2cf47ce65e65f9e48c172cc3b33783359f8e2b2c5f7e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-07T13:28:46Z","title_canon_sha256":"701ab932dac5f7dbc14fe55510f82e543b15d8ca43ba32d47d6f0e0adb008d9d"},"schema_version":"1.0","source":{"id":"1711.03006","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03006","created_at":"2026-07-05T01:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03006v2","created_at":"2026-07-05T01:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03006","created_at":"2026-07-05T01:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"2KPS37VPCBA2","created_at":"2026-07-05T01:09:54Z"},{"alias_kind":"pith_short_16","alias_value":"2KPS37VPCBA2OOHK","created_at":"2026-07-05T01:09:54Z"},{"alias_kind":"pith_short_8","alias_value":"2KPS37VP","created_at":"2026-07-05T01:09:54Z"}],"graph_snapshots":[{"event_id":"sha256:f60aaf1a82d6f22c9c5ed5b0a5a738cc81cb32791203b1bcc24860d81cee40fa","target":"graph","created_at":"2026-07-05T01:09:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1711.03006/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We demonstrate how the asymptotics for large $|z|$ of the generalised Bessel function \\[{}_0\\Psi_1(z)=\\sum_{n=0}^\\infty\\frac{z^n}{\\Gamma(an+b) n!},\\] where $a>-1$ and $b$ is any number (real or complex), may be obtained by exploiting the well-established asymptotic theory of the generalised Wright function ${}_p\\Psi_q(z)$. A summary of this theory is given and an algorithm for determining the coefficients in the associated exponential expansions is discussed in an appendix. We pay particular attention to the case $a=-1/2$, where the expansion for $z\\to\\pm\\infty$ consists of an exponentially sm","authors_text":"R B Paris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-07T13:28:46Z","title":"The asymptotics of the generalised Bessel function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03006","kind":"arxiv","version":2},"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:b8575750477b1393b46a794040816258e11debc5f71439d6b1b988a1ea06db4c","target":"record","created_at":"2026-07-05T01:09:54Z","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":"e345971483b2dcf7a7c2cf47ce65e65f9e48c172cc3b33783359f8e2b2c5f7e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-07T13:28:46Z","title_canon_sha256":"701ab932dac5f7dbc14fe55510f82e543b15d8ca43ba32d47d6f0e0adb008d9d"},"schema_version":"1.0","source":{"id":"1711.03006","kind":"arxiv","version":2}},"canonical_sha256":"d29f2dfeaf1041a738eaec3c79b3210d2392181d1f6026794c274c03d981320d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d29f2dfeaf1041a738eaec3c79b3210d2392181d1f6026794c274c03d981320d","first_computed_at":"2026-07-05T01:09:54.441270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:09:54.441270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c6DaLI0R80ss3XD0i3KTg/zvEJtRsYDgvLxIhi8wGTGuLkf5XnhlWKn6xEk6Ou9oCBcOjOHQXZg/6QnTwmy3DA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:09:54.441700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.03006","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8575750477b1393b46a794040816258e11debc5f71439d6b1b988a1ea06db4c","sha256:f60aaf1a82d6f22c9c5ed5b0a5a738cc81cb32791203b1bcc24860d81cee40fa"],"state_sha256":"f8bb989f0ef5d9e975346ecba7dc4adada19f9d557318cb715e4a2fe758d247c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VzQWMN3pE/TvkjrqzT+8UGZ0WOGovxDYBmFmFYcHr/Okj20aIBb5XerM32Y2zzbf3GEPck3Nau0alYm7RKYaDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T13:26:29.126131Z","bundle_sha256":"3db4a3ec776ad5dba18525e6ad6817cfafd2ade8c1c4bdc62ae445cde8df0808"}}