Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 345-354 https://doi.org/10.4134/BKMS.b190236 Published online August 20, 2019 Printed March 31, 2020

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 \[\sum_{n=-\infty}^\infty\frac{(a;q)_n}{(b;q)_n}z^n.\]