Hypergeometric Generating Function of L-function, Slater's Identities,   and Quantum Invariant
  We study certain connections between the quantum invariants of the torus knots T_{3,2^k} and some q-series identities. In particular, we obtain new generalizations of Slater's identities (83) and (86). 
Kazuhiro Hikami and Anatol N. Kirillov