Note on modular equations in the theory of signature 4

Abstract

AbstractIn 2009, M. S. M. Naika et al. obtained Schl$$\ddot{a}$$ a ¨ fli type modular equations of degree 4. Motivated by their work, in the present work, we prove a class of modular equations in Ramanujan’s alternative theory of elliptic functions using theory of signature 4. In particular, the composite degrees of modular equations {1, 2, 4}, {1, 3, 9}, {1, 5, 25} and {1, 7, 49}.