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 2ψ2 series ∞ ∑ n=−∞ (a, c; q)n (b, d; q)n z and Ramanujan’s sum ∞ ∑ n=−∞ (a; q)n (b; q)n z.