Summations for basic hypergeometric series involving a q-analogue of the digamma function

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.