Several transformation formulas for basic hypergeometric series
Abstract
In 1981, Andrews gave a four-variable generalization of Ramanujan's 11 summation formula. We establish a six-variable generalization of Andrews' identity according to the transformation formula for two 8φ7 series and Bailey's transformation formula for three 8φ7 series. Then it is used to find a six-variable generalization of Ramanujan's reciprocity theorem, which is different from Liu's formula. We derive the generalizations of Bailey's two 33 summation formulas in terms of two limiting relations and Bailey's another transformation formula for three 8φ7 series. Based on the two limiting relations, some different results involving bilateral basic hypergeometric series are also deduced from the Guo--Schlosser transformation formula and other two transformation formulas.