In this paper, we study properties of the coefficients appearing in the q-series expansion of ∏n ≥1 [(1 − qn) ∕ (1 − qpn)] δ, the infinite Borwein product for an arbitrary prime p, raised to an arbitrary positive real power δ. We use the Hardy-Ramanujan-Rademacher circle method to give an asymptotic formula for the coefficients. For p = 3 we give an estimate of their growth which enables us to partially confirm an earlier conjecture of the first author concerning an observed sign pattern of the coefficients when the exponent δ is within a specified range of positive real numbers. We further establish some vanishing and divisibility properties of the coefficients of the cube of the infinite Borwein product.
The following version is available: