Quadratic transformation formulas for basic hypergeometric series
Mizan Rahman, Arun Verma
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Source: Crossref
Published: Jan 1, 1993
DOI: 10.1090/s0002-9947-1993-1074149-8
Open original source ↗Source abstract
Starting with some of the known transformation formulas for well-poised 2 ϕ 1 _2{\phi _1} and very-well-poised 8 ϕ 7 _8{\phi _7} basic hypergeometric series we obtain q q -analogues of 36 36 quadratic transformation formulas given in § 2.11 \S 2.11 of Higher transcendental functions , Vol. 1, edited by Erdélyi et al. We also derive some new quadratic transformation formulas that give rise to identities connecting very-well-poised but unbalanced 10 ϕ 9 _{10}{\phi _9} series in base q q with very-well-poised and balanced 12 ϕ 11 _{12}{\phi _{11}} series in base q 2 {q^2} . A Rogers-Ramanujan type identity is also found as a limiting case.
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