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 On four new mock theta functions Bull. Korean Math. Soc.Published online August 20, 2019 Qiuxia Hu Shanghai Normal University Abstract : In this paper, we first give some representations for four new mock theta functions defined by Andrews \cite{Andrews} and Bringmann, Hikami and Lovejoy \cite{BHL} using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of $_2\psi_2$ series $\sum_{n=-\infty}^\infty\frac{(a,c;q)_n}{(b,d;q)_n}z^n$ and Ramanujan's sum $\sum_{n=-\infty}^\infty\frac{(a;q)_n}{(b;q)_n}z^n.$ Keywords : Mock theta functions; divisor sums; basic bilateral hypergeometric series MSC numbers : 11F37 Full-Text :