Analogues of Jacobi's inversion formula for the incomplete elliptic integral of the first kind

AbstractIn this article, we revisit Ramanujan's cubic analogue of Jacobi's inversion formula for the classical elliptic integral of the first kind. Our work is motivated by the recent work of Milne (Ramanujan J. 6(1) (2002) 7–149), Chan and Chua (Ramanujan J., to appear) on the representations of integers as sums of even squares