 Since mock theta functions can be expressed in terms of Appell–Lerch series this means that mock theta functions transform like modular forms if they have a certain non-analytic series added to them.showed that several of Ramanujan's fifth order mock theta functions are equal to quotients Θ(τ)/θ(τ) where θ(τ) is a modular form of weight 1/2 and Θ(τ) is a theta function of an indefinite binary quadratic form, and proved similar results for seventh order mock theta functions.Zwegers showed how to complete the indefinite theta functions to produce real analytic modular forms, and used this to give another proof of the relation between mock theta functions and weak Maass wave forms.