Perturbed Hankel determinant, correlation functions and Painlevé equations

Min Chen, Yang Chen, Engui Fan

We continue with the study of the Hankel determinant, $$D_n(t,\alpha ,\beta ):=\det {\left({\int }_0^1{x}^{j+k}w(x;t,\alpha ,\beta )dx\right)}_{j,k=0}^{n-1},$$ generated by a Pollaczek-Jacobi type weigh…