The number of strongly unimodal sequences of weight n is denoted by u * (n). The generating functions for {u * (n)} ∞ n=1 are U * (q) = ∞ n=1 u * (n)q n . Rhoades recently gave a precise asymptotic for u * (n) by expressing U * (q) as a mixed mock modular form. In this note, by revisiting the mixed mock modular form associated to U * (q), three new mixed mock modular forms are constructed by considering the bilateral series of U * (q) and the third order Ramanujan's mock theta function f (q).

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... e inner relationships among them are discussed although they are defined in different ways. These new mixed mock modular forms can be expressed in terms of Appell-Lerch sums. The related mock theta functions can be completed as harmonic weak Maass forms. As an application, we give a proof for the claim by Bajpai et al. that the bilateral series B(f ; q) of the third order mock theta function f (q) is a mixed mock modular form.