We continue with the study of the Hankel determinant, defined by, D n (t, α) = det ∞ 0 x j+k w(x; t, α)dx n−1 j,k=0 , generated by a singularly perturbed Laguerre weight, w(x; t, α) = x α e −x e −t/x , x ∈ R + , α > 0, t > 0, obtained through a deformation of the Laguerre weight function, w(x; 0, α) = x α e −x , x ∈ R + , α > 0, via the multiplicative factor e −t/x . An earlier investigation was made on the finite n aspect of such determinants, which appeared in [20]. It was found that the logarithm of the Hankel determinant has an integral representation in terms of a particular Painlevé III( P III , for short) and its t derivatives. In this paper we show that, under a double scaling, where n , the order of the Hankel matrix tends to ∞, and t , tends to 0 + , the scaled-and therefore, in some sense, infinite dimensional-Hankel determinant, has an integral representation in terms of a C potential. The second order non-linear ode satisfied by C, after a change of variable, is another P III transcendent, albeit with fewer number of parameters. Expansions of the double scaled determinant for small and large parameter are oband Telephone:(853)8822-8546.