| In his famous paper "Modular equations and approximations to£k," Ramanujan¡]1914¡^offered 17 beautiful series for . Although some of his series and ideas contained therein have recently been implemented to compute millions or billions digits of £k, the underlying theory has not been fully developed. After the recent work of Borwein and Borwein¡]1987¡^and of B.C.Berndt, S.Bhargava,and F.G.Garvan¡]1995¡^, the aforementioned theory it now known as Ramanujan's theory of elliptic functions to alternative bases. In this work, we will see how one can derive new Ramanujan-type series of 1/£k. Using the alternative bases theory, Kronecker's limit formula, and our recent work on cubic modular equations, we add eighteen new series to the list. One of our new series gives approximately 33 additional digits per term-the fastest convergent series belonging to the theory of alternative base 3 known so far. |