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Several \(q\)-series identities from the Euler expansions of \((a;q)_{\infty }\) and \(\frac {1}{(a;q)_{\infty }}\). (English) Zbl 1212.05017

Summary: We first give several operator identities which extend the results of Chen and Liu, then make use of them to two \(q\)-series identities obtained by the Euler expansions of \((a;q)_{\infty }\) and \(1/(a;q)_{\infty }\). Several \(q\)-series identities are obtained involving a \(q\)-series identity in Ramanujan’s Lost Notebook.

MSC:

05A30 \(q\)-calculus and related topics
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
33D60 Basic hypergeometric integrals and functions defined by them
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