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.
CHEN, XIAOJING and CHU, WENCHANG
"$Q$-analogues of five difficult hypergeometric evaluations,"
Turkish Journal of Mathematics: Vol. 44:
3, Article 12.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss3/12