Recently, Schlosser and Zhou proposed many conjectures on sign patterns of the coefficients appearing in the q-series expansions of the infinite Borwein product and other infinite products raised to a real power. In this paper, we will study several of these conjectures. Let \ G (q): =₈=₁^I (₊=₀^ (1-q^m₈+kn₈) (1-q^-m₈+ (k+1) n₈) ) ^u₈ \ where I is a positive integer, 1 m₈<n₈ and u₈0 for 1 i I and |q|<1. We will establish an asymptotic formula for the coefficients of G (q) ^δ with δ being a positive real number by using the Hardy--Ramanujan--Rademacher circle method. As applications, we apply the asymptotic formula to confirm some of the conjectures of Schlosser and Zhou.
He et al. (2025) studied this question.