Certain Second Order Nonlinear differential equations involving k- functions

Abstract

Ramanujan documented different levels of beautiful Eisenstein series relations in his notebooks. Recently, Shaun Cooper in his book noted several identities involving Eisenstein series and k-functions. In this paper, certain second order nonlinear differential identities have been established, which involves k- functions. Further, the convolution sum has been evaluated using Eisenstein series of level 5 and 10.