This paper contain results on a strange smallest parts function related to the second Atkin-Garvan moment. Some new identities are discovered in relation to Andrews spt function as well as one of Borweins' two-dimensional theta functions.

a b s t r a c tWe provide some further theorems on the partitions generated by the rank parity function. New Bailey pairs are established, which are of independent interest.

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We provide a new approach to establishing certain q-series identities that were proved by Andrews, and show how to prove further identities using conjugate Bailey pairs. Some relations between some q-series and ternary quadratic forms are established.

In this paper we offer some new identities associated with mock theta functions and establish new Bailey pairs related to indefinite quadratic forms. We believe our proof is instructive use of changing base of Bailey pairs, and offers new information on some Bailey pairs that have proven important in the study of Mock theta functions.