On second order mock theta function $ B(q) $

In this paper, we present some arithmetic properties for the second order mock theta function $ B(q) $ given by McIntosh as: \begin{document}$ B(q) = \sum\limits_{n = 0}^{\infty}\frac{q^n(-q;q^2)_n}{(q;q^2)_{n+1}}. $\end{document}