$Q$-analogues of five difficult hypergeometric evaluations

Authors: XIAOJING CHEN, WENCHANG CHU

Abstract: A nonterminating balanced $q$-series is examined by means of the modified Abel lemma on summation by parts that leads to $q$-analogues of five difficult identities for classical hypergeometric series, including three formulae conjectured by Gosper in 1977.

Keywords: Abel's lemma on summation by parts,classical hyper geometric series,basic hyper geometric series,balanced series, bilateral series, the gamma function

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