Summations for basic hypergeometric series involving a \(q\)-analogue of the digamma function (Q1816671)

Using a simple method, numerous summation formulas for hypergeometric and basic hypergeometric series are derived. Among these summation formulas are nonterminating extensions and \(q\)-extensions of identities recorded by Lavoie, Luke, Watson, and Srivastava. At the result side of the basic hypergeometric summations, there appears a \(q\)-analogue of the digamma function. Some of its properties are also studied. Various special and limit cases of the results presented in this paper are discussed.