SOME MATCHING COEFFICIENTS OF $q-$PRODUCTS

We find some results on matching coefficients for certain $q$-products. Some of the results are associated with Rogers$-$Ramanujan continued fraction $$R(q)=\frac{(q,q^4;q^5)_{\infty}}{(q^2,q^3;q^5)_{\infty}},$$ while some are associated with analogous of Rogers$-$Ramanujan functions. The techniques used for proving the results involves Ramanujan's theta functions, identities for Rogers$-$Ramanujan type functions, and $q$-series manipulations.