Quite recently, the first author investigated vanishing coefficients of the arithmetic progressions in several q-series expansions. In this paper, we further study the signs of coefficients in two q-series expansions and establish some interlinked identities for several q-series expansions by means of Ramanujan’s theta functions. We obtain the 5-dissections of these two q-series and give combinatorial interpretations for these dissections. Moreover, we obtain four q-series identities involving the aforementioned q-series, two of which were proved by Kim and Toh via modular forms.
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The authors are indebted to Shishuo Fu for his helpful comments on a preliminary version of this paper. The authors also would like to thank the anonymous referee for his/her careful reading and helpful comments on an earlier version of the paper.