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The aim of the present paper is to obtain lower bounds for $\\mathcal{R} \\left\\{ \\frac{w_{\\alpha ,v}(z)}{\\left( w_{\\alpha ,v}\\right) _{m}(z)}\\right\\} ,$ $\\mathcal{R}\\left\\{ \\frac{\\left( w_{\\alpha ,v}\\right) _{m}(z)}{w_{\\alpha ,v}(z)}\\right\\} ,$ $\\mathcal{R}\\left\\{ \\frac{w_{\\alpha ,v}^{^{\\pr"},"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":"1606.05906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-19T20:39:46Z","cross_cats_sorted":[],"title_canon_sha256":"b97686a6abcec105df757d351797234901545515ce14fe44032d7ce5f9aa0349","abstract_canon_sha256":"5f12b61c0dfad33f80c406df6d8763ec199b941e494a212c1a76bccae6d18c5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:15.841751Z","signature_b64":"LCBJUgOGjgCiZcdnBqN56V63W37NPOdsnc9DnIfcEWT9kAHA+9AXD2ln8f/ZP++t8rNRwhffq1gAPac/8UKxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b67f9597b088033bc1be20b60da927751a52ec87f528d470530d388113d57af8","last_reissued_at":"2026-05-18T01:12:15.841374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:15.841374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partial sums of the normalized Dini functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Halit Orhan, \\.Ibrahim Akta\\c{s}","submitted_at":"2016-06-19T20:39:46Z","abstract_excerpt":"Let $\\left( w_{\\alpha ,v}\\right) _{m}(z)=z+\\sum\\limits_{n=1}^{m}a_{n}z^{n+1} $ be the sequence of partial sums of normalized Dini functions $w_{\\alpha ,v}(z)=z+\\sum\\limits_{n=1}^{\\infty }a_{n}z^{n+1}$ where $a_{n}=\\frac{\\left( -1\\right) ^{n}\\left( 2n+\\alpha \\right) }{\\alpha 4^{n}n!\\left( v+1\\right) _{n}% }$. The aim of the present paper is to obtain lower bounds for $\\mathcal{R} \\left\\{ \\frac{w_{\\alpha ,v}(z)}{\\left( w_{\\alpha ,v}\\right) _{m}(z)}\\right\\} ,$ $\\mathcal{R}\\left\\{ \\frac{\\left( w_{\\alpha ,v}\\right) _{m}(z)}{w_{\\alpha ,v}(z)}\\right\\} ,$ $\\mathcal{R}\\left\\{ \\frac{w_{\\alpha ,v}^{^{\\pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05906","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":"1606.05906","created_at":"2026-05-18T01:12:15.841421+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.05906v1","created_at":"2026-05-18T01:12:15.841421+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05906","created_at":"2026-05-18T01:12:15.841421+00:00"},{"alias_kind":"pith_short_12","alias_value":"WZ7ZLF5QRABT","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"WZ7ZLF5QRABTXQN6","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"WZ7ZLF5Q","created_at":"2026-05-18T12:30:51.357362+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/WZ7ZLF5QRABTXQN6EC3A3KJHOU","json":"https://pith.science/pith/WZ7ZLF5QRABTXQN6EC3A3KJHOU.json","graph_json":"https://pith.science/api/pith-number/WZ7ZLF5QRABTXQN6EC3A3KJHOU/graph.json","events_json":"https://pith.science/api/pith-number/WZ7ZLF5QRABTXQN6EC3A3KJHOU/events.json","paper":"https://pith.science/paper/WZ7ZLF5Q"},"agent_actions":{"view_html":"https://pith.science/pith/WZ7ZLF5QRABTXQN6EC3A3KJHOU","download_json":"https://pith.science/pith/WZ7ZLF5QRABTXQN6EC3A3KJHOU.json","view_paper":"https://pith.science/paper/WZ7ZLF5Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.05906&json=true","fetch_graph":"https://pith.science/api/pith-number/WZ7ZLF5QRABTXQN6EC3A3KJHOU/graph.json","fetch_events":"https://pith.science/api/pith-number/WZ7ZLF5QRABTXQN6EC3A3KJHOU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WZ7ZLF5QRABTXQN6EC3A3KJHOU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WZ7ZLF5QRABTXQN6EC3A3KJHOU/action/storage_attestation","attest_author":"https://pith.science/pith/WZ7ZLF5QRABTXQN6EC3A3KJHOU/action/author_attestation","sign_citation":"https://pith.science/pith/WZ7ZLF5QRABTXQN6EC3A3KJHOU/action/citation_signature","submit_replication":"https://pith.science/pith/WZ7ZLF5QRABTXQN6EC3A3KJHOU/action/replication_record"}},"created_at":"2026-05-18T01:12:15.841421+00:00","updated_at":"2026-05-18T01:12:15.841421+00:00"}