ON FOUR NEW MOCK THETA FUNCTIONS

In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] 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 Sigma(n = -infinity) (infinity) (a, c; q)(n) / (b, d; q)(n) z(n) and Ramanujan's sum Sigma(n = -infinity) (infinity) (a; q)(n) / (b; q)(n) z(n).