The smallest eigenvalue of large Hankel matrices generated by a singularly perturbed Laguerre weight
The smallest eigenvalue of large Hankel matrices generated by a singularly perturbed Laguerre weight
An asymptotic expression of the orthonormal polynomials PN(z) as N → ∞, associated with the singularly perturbed Laguerre weight wα(x;t)=xαe−x−tx,x∈[0,∞),α>−1,t≥0, is derived. Based on this, we establish the asymptotic behavior of the smallest eigenvalue, λN, of the Hankel matrix generated by the weight wα(x; t).