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Borwein-Bradley-type identities for Ramanujan-type series for $1/π^4$ — arXiv:2610.04770

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.04770
License (as archived): CC0-1.0
Archived: 2026-10-06T16:53:06.809Z
SHA-256 of the archived text: 0a94cdde63aaad96c051e951ca6d24e44fa8a2ff71760d9fcf7506ab5fa5726c
Stable URL of this page: https://metraipolis.com/documento/dc_fc2d83e4f033

How to cite

Borwein-Bradley-type identities for Ramanujan-type series for $1/π^4$ — arXiv:2610.04770 — arXiv (en), https://arxiv.org/abs/2610.04770 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fc2d83e4f033 (Metraipolis archive dc_fc2d83e4f033, sha256 0a94cdde63aaad96c051e951ca6d24e44fa8a2ff71760d9fcf7506ab5fa5726c)

BibTeX

@misc{dcfc2d83e4f033,
  title = {Borwein-Bradley-type identities for Ramanujan-type series for $1/π^4$ — arXiv:2610.04770},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.04770},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fc2d83e4f033; sha256 0a94cdde63aaad96c051e951ca6d24e44fa8a2ff71760d9fcf7506ab5fa5726c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.04770. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove ten conjectures of Z.-W. Sun on Ramanujan-type series for $1/\pi^4$ and $\pi^4$ with harmonic numbers. They follow by comparing Taylor coefficients in new Borwein-Bradley-type identities, whose products depend only on $x^3$, $x^4$, $x^6$ or $x^8$. These identities come from parametric extensions of the series of Cullen and Zhao. We derive the extensions from K. C. Au's Wilf-Zeilberger (WZ) seeds, and their sums are trigonometric. Our proofs use Guillera's periodicity argument and give new proofs of the original series. In the same way, Dougall's $_5F_4$ sum gives half-integer analogues of the identities of Koecher, Borwein-Bradley and Cohen, whose Taylor coefficients are Apéry-like series for products of zeta values.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Number Theory (math.NT) ; Classical Analysis and ODEs (math.CA); Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2610.04770 — 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 2026-10-06T15:19:20.053Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).