On new identities connecting Ramanujan-Göllnitz-Gordon continued fraction and Ramanujan's continued fraction of order four

Abstract

By employing the classical tools from the theory of $q$-series and theta functions, new fascinating identities on different continued fractions can be achieved. In this article, we use the product expansion of Jacobi's theta function to establish identities that connect Ramanujan-Göllnitz-Gordon continued fraction with Ramanujan's continued fraction of order four. Also, we obtain Lambert series identities using Ramanujan's ${}_1{\psi }_1$ summation formula.