Some identities on the second order mock theta functions

Abstract

Recently, Nath and Das investigated congruence properties for the second order mock theta function $B(q)$. In their paper, they asked for analytic proofs of three identities on the second order mock theta functions $A(q)$, $B(q)$ and $\hat{I}{¼}_2(q)$. In this paper, we settle Nath and Das' open problem by using the $(p,k)$-parametrization of theta functions and several identities due to Hickerson and Mortenson.