{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:X4C7YP2AMHIZF6AETUAMJSCY5C","short_pith_number":"pith:X4C7YP2A","canonical_record":{"source":{"id":"1708.03358","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-10T18:58:10Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4d88962ad9e1363dc0340c00bb6d6655925f975fed556f7e37092df098f42540","abstract_canon_sha256":"ac9a5347ef59b7b49f6cc41976dbb72af19c464800dac127991880863b3db675"},"schema_version":"1.0"},"canonical_sha256":"bf05fc3f4061d192f8049d00c4c858e889f56c1ccef4d0bb9aee2d648e8bfda1","source":{"kind":"arxiv","id":"1708.03358","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03358","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03358v1","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03358","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"X4C7YP2AMHIZ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X4C7YP2AMHIZF6AE","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X4C7YP2A","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:X4C7YP2AMHIZF6AETUAMJSCY5C","target":"record","payload":{"canonical_record":{"source":{"id":"1708.03358","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-10T18:58:10Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4d88962ad9e1363dc0340c00bb6d6655925f975fed556f7e37092df098f42540","abstract_canon_sha256":"ac9a5347ef59b7b49f6cc41976dbb72af19c464800dac127991880863b3db675"},"schema_version":"1.0"},"canonical_sha256":"bf05fc3f4061d192f8049d00c4c858e889f56c1ccef4d0bb9aee2d648e8bfda1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:13.353134Z","signature_b64":"cr8KhOeMI91UdR6ZV27k/hQjwUow8joOEY6Kr4OcwSr9Daf/tIP1tXGba72hRv5rLW17v6XsiZJLtpepwgGTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf05fc3f4061d192f8049d00c4c858e889f56c1ccef4d0bb9aee2d648e8bfda1","last_reissued_at":"2026-05-18T00:38:13.352378Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:13.352378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.03358","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"USQWObUEwzFXaHHhvLXCORRks9TlHT6d79anwmrK3auxCaxB7uJj8n9dRwYUQDev2gyd17AmyrC84rNN9wnDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:05:56.667413Z"},"content_sha256":"9787b6ee61da53cf7ef7c9183e31e32de0d34ee5580460fe9effcf859069e7a8","schema_version":"1.0","event_id":"sha256:9787b6ee61da53cf7ef7c9183e31e32de0d34ee5580460fe9effcf859069e7a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:X4C7YP2AMHIZF6AETUAMJSCY5C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generating function and formulae defining the first-associated Meixner-Pollaczek polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Khalid Ahbli, Zouhair Mouayn","submitted_at":"2017-08-10T18:58:10Z","abstract_excerpt":"While considering nonlinear coherent states with specific anti-holomorphic coefficients $\\bar{z}^n/\\sqrt{x_n!}$, we identify as first associated Meixner-Pollaczek polynomials the orthogonal polynomials arising from shift operators which are defined by the sequence $x_n=(n+1)^2$ . We give a formula defining these polynomials by writing down their generating function. This also leads to construct a Bargmann-type integral transform whose kernel is given in terms of a $\\Psi_1$ Humbert's function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03358","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8sNteCK1d1tDoaYG5hkNnbXCXvWwAuBlvR6M28pgI+LLPTKRriDNNNGaqpZOwl0nLf/tDnW+u3g6v5p8DTHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:05:56.667806Z"},"content_sha256":"4e1977191abbd228528b207cf25073d8a3163f15a92d94048ab2dfce297fe60d","schema_version":"1.0","event_id":"sha256:4e1977191abbd228528b207cf25073d8a3163f15a92d94048ab2dfce297fe60d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X4C7YP2AMHIZF6AETUAMJSCY5C/bundle.json","state_url":"https://pith.science/pith/X4C7YP2AMHIZF6AETUAMJSCY5C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X4C7YP2AMHIZF6AETUAMJSCY5C/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":"2026-06-26T13:05:56Z","links":{"resolver":"https://pith.science/pith/X4C7YP2AMHIZF6AETUAMJSCY5C","bundle":"https://pith.science/pith/X4C7YP2AMHIZF6AETUAMJSCY5C/bundle.json","state":"https://pith.science/pith/X4C7YP2AMHIZF6AETUAMJSCY5C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X4C7YP2AMHIZF6AETUAMJSCY5C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:X4C7YP2AMHIZF6AETUAMJSCY5C","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":"ac9a5347ef59b7b49f6cc41976dbb72af19c464800dac127991880863b3db675","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-10T18:58:10Z","title_canon_sha256":"4d88962ad9e1363dc0340c00bb6d6655925f975fed556f7e37092df098f42540"},"schema_version":"1.0","source":{"id":"1708.03358","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03358","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03358v1","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03358","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"X4C7YP2AMHIZ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X4C7YP2AMHIZF6AE","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X4C7YP2A","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:4e1977191abbd228528b207cf25073d8a3163f15a92d94048ab2dfce297fe60d","target":"graph","created_at":"2026-05-18T00:38:13Z","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":"While considering nonlinear coherent states with specific anti-holomorphic coefficients $\\bar{z}^n/\\sqrt{x_n!}$, we identify as first associated Meixner-Pollaczek polynomials the orthogonal polynomials arising from shift operators which are defined by the sequence $x_n=(n+1)^2$ . We give a formula defining these polynomials by writing down their generating function. This also leads to construct a Bargmann-type integral transform whose kernel is given in terms of a $\\Psi_1$ Humbert's function.","authors_text":"Khalid Ahbli, Zouhair Mouayn","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-10T18:58:10Z","title":"A generating function and formulae defining the first-associated Meixner-Pollaczek polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03358","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":"sha256:9787b6ee61da53cf7ef7c9183e31e32de0d34ee5580460fe9effcf859069e7a8","target":"record","created_at":"2026-05-18T00:38:13Z","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":"ac9a5347ef59b7b49f6cc41976dbb72af19c464800dac127991880863b3db675","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-10T18:58:10Z","title_canon_sha256":"4d88962ad9e1363dc0340c00bb6d6655925f975fed556f7e37092df098f42540"},"schema_version":"1.0","source":{"id":"1708.03358","kind":"arxiv","version":1}},"canonical_sha256":"bf05fc3f4061d192f8049d00c4c858e889f56c1ccef4d0bb9aee2d648e8bfda1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf05fc3f4061d192f8049d00c4c858e889f56c1ccef4d0bb9aee2d648e8bfda1","first_computed_at":"2026-05-18T00:38:13.352378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:13.352378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cr8KhOeMI91UdR6ZV27k/hQjwUow8joOEY6Kr4OcwSr9Daf/tIP1tXGba72hRv5rLW17v6XsiZJLtpepwgGTBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:13.353134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03358","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9787b6ee61da53cf7ef7c9183e31e32de0d34ee5580460fe9effcf859069e7a8","sha256:4e1977191abbd228528b207cf25073d8a3163f15a92d94048ab2dfce297fe60d"],"state_sha256":"b5021dcb387822dda4991a62eb3fc5103680e5d27e977787938e957b32649e50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXu3SMZ8Qiisb39Zy5xAP5eTvoBh7S5IFSMZWpIOCgQA/GK0ZV7PN4CrgUX99suhG7VQ++HT7Pj+h1vGM1VHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T13:05:56.669749Z","bundle_sha256":"41fa8ad475a10750552cf4cdad3a83c067f8ad156c9b6ba25107bb6bace210bf"}}