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Schmidt","submitted_at":"2017-04-18T04:33:23Z","abstract_excerpt":"We construct new continued fraction expansions of Jacobi-type J-fractions in $z$ whose power series expansions generate the ratio of the $q$-Pochhamer symbols, $(a; q)_n / (b; q)_n$, for all integers $n \\geq 0$ and where $a,b,q \\in \\mathbb{C}$ are non-zero and defined such that $|q| < 1$ and $|b/a| < |z| < 1$. If we set the parameters $(a, b) := (q, q^2)$ in these generalized series expansions, then we have a corresponding J-fraction enumerating the sequence of terms $(1-q) / (1-q^{n+1})$ over all integers $n \\geq 0$. Thus we are able to define new $q$-series expansions which correspond to the"},"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":"1704.05200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-18T04:33:23Z","cross_cats_sorted":[],"title_canon_sha256":"a5760f147570881fad47bbf432a716568e430509d45f7436bc6a206bfc51670c","abstract_canon_sha256":"0949803965fea66621d27e069b182a037f9f935a31c4b4faf2956085802429e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:06.599452Z","signature_b64":"EywBB+mL5eERqFGFPQ/qafHKqgv32s4Llcaq15p+dCteI/z6zDQEKphiWjqgJrh0JAK4MN6ZIPQ2+c3ty5vqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5acc8dfb7cc2552108d62dee4a480701033c0a6f70d176db78732f71d34adae","last_reissued_at":"2026-05-18T00:39:06.598887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:06.598887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continued Fractions and $q$-Series Generating Functions for the Generalized Sum-of-Divisors Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maxie D. Schmidt","submitted_at":"2017-04-18T04:33:23Z","abstract_excerpt":"We construct new continued fraction expansions of Jacobi-type J-fractions in $z$ whose power series expansions generate the ratio of the $q$-Pochhamer symbols, $(a; q)_n / (b; q)_n$, for all integers $n \\geq 0$ and where $a,b,q \\in \\mathbb{C}$ are non-zero and defined such that $|q| < 1$ and $|b/a| < |z| < 1$. If we set the parameters $(a, b) := (q, q^2)$ in these generalized series expansions, then we have a corresponding J-fraction enumerating the sequence of terms $(1-q) / (1-q^{n+1})$ over all integers $n \\geq 0$. 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