Several transformation formulas for basic hypergeometric series

DOI10.1080/10236198.2021.1876683zbMath1465.33013arXiv1301.4476OpenAlexW3125626711MaRDI QIDQ4991836

Chuanan Wei, Dian Xuan Gong

Publication date: 4 June 2021

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.4476

zbMATH Keywords

basic hypergeometric seriesRamanujan's reciprocity theoremRamanujan's \(_1\psi_1\) summation formulaAndrews' identity

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Cites Work

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• Extensions of Ramanujan's reciprocity theorem and the Andrews-Askey integral
• Six-variable generalization of Ramanujan's reciprocity theorem and its variants
• Ramanujan's ``lost notebook. I: Partial Theta-functions
• Some operator identities and \(q\)-series transformation formulas
• A common \(q\)-analogue of two supercongruences
• \(q\)-analogues of Dwork-type supercongruences
• A reciprocity theorem for certain \(q\)-series found in Ramanujan's lost notebook
• On the bilateral series \({}_5\psi_5\)
• Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series
• Generalizations of Ramanujan's reciprocity theorem and their applications

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