Let K_(m,p) denote the family of double twist knots where 2m-1 and 2p are non-zero integers denoting the number of half-twists in each region. Using a result of Takata, we prove a formula for the colored Jones polynomial of K_(-m,-p) and
K_(-m,p). The latter case leads to new families of q-hypergeometric series generalizing the Kontsevich-Zagier series. These generalized Kontsevich-Zagier series are conjectured to be quantum modular forms. We also use Bailey pairs and formulas of Walsh to find Habiro-type expansions for the colored Jones polynomials of K_(m,p) and K_(m,-p).

The authors would like to thank Paul Beirne and Katherine Walsh Hall for their helpful comments and suggestions. The second author would like to thank the Max-Planck-Institut für Mathematik for their support during the completion of this paper.