Ramanujan's inversion formulas for the lemniscate and allied functions (Q1192549)

The authors prove ten formulas from Ramanujan's second notebook that involve the inverse of the lemniscate function \[ F(v) := \int_ 0^ v {dt \over \sqrt{1-t^ 4}} \] and two other similar functions: \( \int_ 0^ v {dt / \sqrt{1+t^ 4}}\), and \( \int_ 0^ v {dt / \sqrt{1-t^ 6}}. \) Both the classical theory of elliptic integrals and Weierstrass theory are used in the proofs.