Abstract

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.

Keywords and Phrases

Matching coefficient, $q$-product, Rogers$-$Ramanujan continued fraction, Rogers$-$Ramanujan type functions.

A.M.S. subject classification

11A55, 11F33.

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