Modular identities for some special cases of Ramanujan’s general continued fraction

In this article, we first introduce the continued fractions K(q), L(q) and M(q), which are based on the Ramanujan-Selberg continued fraction C(q). We then obtain several modular identities which connect K(q) with K(-q) and K(qi)(i=2,3,5,7), L(q) with L(-q) and L(qj)(j=2,3), M(q) with M(-q) and M(qj)(j=2,3), and C(q) with C(-q). We also provide some algebraic results associated with K(q) and L(q). In addition, as an application of our results, we deduce a few fascinating colored partitions which also validate the results.