Jacobi-Sohncke Type Mixed Modular Equations And Their Applications

In this paper, we establish Jacobi-Sohncke type several new mixed modular equations for composite degrees 1, 3, $n$ and $3n$. As an application, we establish the modular relations between the Ramanujan-Selberg continued fractions $H(q),\ H(q^3),\ H(q^n)$ and $H(q^{3n})$ for $n=2,3,4,5,7,9,11$ and also we obtain congruence relations for color overpartitions of $n$ with odd parts.