Communications of the
Korean Mathematical Society CKMS

The authors aim mainly at giving fifteen three-term contiguous relations for the basic hypergeometric series ${}_2 \phi_1$ corresponding to Gauss's contiguous relations for the hypergeometric series ${}_{2}F_{1}$ given in Rainville([6], p.71). They also apply them to obtain two summation formulas closely related to a known $q$-analogue of Kummer's theorem.

Keywords: basic hypergeometric series, $q$-analogue of Kummer's summation theorem, Gauss's summation theorem, Gauss's contiguous relations

MSC numbers: Primary 33C20; Secondary 33D05, 33D