Communications of the
Korean Mathematical Society CKMS

We obtain recursion formulas for $q$-hypergeometric and $q$-Appell series. We also find recursion formulas for the general double $q$-hypergeometric series. It is shown that these recursion relations can be expressed in terms of $q$-derivatives of the respective $q$-hypergeometric series.

Keywords: recursion formulas, generalized basic hypergeometric series, $q$-Appell series, general double $q$-hypergeometric series

MSC numbers: Primary 33D15, 33D70