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Parameterized partial theta identities and a unified $q$-difference proof — arXiv:2609.07245

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.07245
License (as archived): CC0-1.0
Archived: 2026-10-16T14:49:21.061Z
SHA-256 of the archived text: d56a195bd19f6b2085f057d8037e412faf3fec7ab1d50f1ced9d5ca22137086e
Stable URL of this page: https://metraipolis.com/documento/dc_33be60b702bb

How to cite

Parameterized partial theta identities and a unified $q$-difference proof — arXiv:2609.07245 — arXiv (en), https://arxiv.org/abs/2609.07245 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_33be60b702bb (Metraipolis archive dc_33be60b702bb, sha256 d56a195bd19f6b2085f057d8037e412faf3fec7ab1d50f1ced9d5ca22137086e)

BibTeX

@misc{dc33be60b702bb,
  title = {Parameterized partial theta identities and a unified $q$-difference proof — arXiv:2609.07245},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.07245},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_33be60b702bb; sha256 d56a195bd19f6b2085f057d8037e412faf3fec7ab1d50f1ced9d5ca22137086e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.07245. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We establish five families of integer-parameter extensions of Ramanujan's partial theta identities. The families follow from a common two-parameter specialization of Andrews' transformation, for which we give an independent proof based on a $q$-difference recurrence and a boundary estimate. Specializations of the integer parameter recover six identities from Ramanujan's lost notebook. As an application, a residue argument applied to the fifth family gives an integer-parameter extension of Lovejoy's residual identity, from which we construct a corresponding family of conjugate Bailey pairs.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.CO).
Categorie arXiv: Number Theory (math.NT) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.07245 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T14:32:29.927Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).