In this paper, we consider the perturbed Laguerre unitary ensemble described by the weight function of w(x,t)=(x+t)λxαe−x with x≥0, t>0, α>0, α+λ+1>0. The Deift-Zhou nonlinear steepest descent approach is used to analyze the limit of the eigenvalue correlation kernel... was found that under the double scaling s=4nt, n→∞, t→0 such that s is positive and finite, at the hard edge, ...