Abstract

We introduce a new general conjugate Bailey pair which bridges the gap between Bailey and Slater’s work and the work done recently by Andrews and Warnaar. With this new general pair we are able to find many useful conjugate Bailey pairs similar to those of Andrews and Warnaar. Using our new pairs we show results related to the sums of triangular numbers, indefinite quadratic forms and partition identities. We close with a brief discussion of the many other paths that can and will be taken in the future.

Keywords

basic hypergeometric series, conjugate Bailey pairs

Mathematical Subject Classification

Primary: 05A19, 11P82, 05A18, 33D15

Authors