Two generalizations of Jacobi’s triple product identity and their applications

Wei, Chuanan; Yu, Yuanbo; Hu, Qiuxia

doi:10.1007/s11139-022-00640-x

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2023

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“…We expect that more identities of this kind can be found. (In fact, after an earlier version of this paper appeared as a preprint, some results were established in [57] which are closely related to Theorem 2.1 and the results described in Remark 2.2.) Their very compact form and beauty suggests that these objects merit further study.…”

Section: Discussionmentioning

confidence: 73%

Bilateral identities of the Rogers–Ramanujan type

Schlosser

2023

Trans. Amer. Math. Soc. Ser. B

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We derive by analytic means a number of bilateral identities of the Rogers–Ramanujan type. Our results include bilateral extensions of the Rogers–Ramanujan and the Göllnitz–Gordon identities, and of related identities by Ramanujan, Jackson, and Slater. We give corresponding results for multisums including multilateral extensions of the Andrews–Gordon identities, of the Andrews–Bressoud generalization of the Göllnitz–Gordon identities, of Bressoud’s even modulus identities, and other identities. Our closed form bilateral and multilateral summations appear to be the very first of their kind.

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Section: Discussionmentioning

confidence: 73%

Bilateral identities of the Rogers–Ramanujan type

Schlosser

2023

Trans. Amer. Math. Soc. Ser. B

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Two generalizations of Jacobi’s triple product identity and their applications

Cited by 1 publication

References 22 publications

Bilateral identities of the Rogers–Ramanujan type

Bilateral identities of the Rogers–Ramanujan type

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