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We construct eta-quotient representations of two families of q-series involving the Rogers–Ramanujan continued fraction by establishing related recurrence relations. We also display how these eta-quotient representations can be utilised to dissect certain q-series identities.
Following recent investigations of vanishing coefficients in infinite products, we show that such instances are very rare when the infinite product is among a family of theta-quotients of modulus five. We also prove that a general family of products of theta functions of modulus five can always be effectively 5-dissected.
where $[x]$ denotes the integral part of real $x$. The above summations were recently considered by Bordellès et al. [‘On a sum involving the Euler function’, Preprint, 2018, arXiv:1808.00188] and Wu [‘On a sum involving the Euler totient function’, Preprint, 2018, hal-01884018].
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