Exceptional solutions to the Painleve VI equation associated with the generalized Jacobi weight

We consider the generalized Jacobi weight x(alpha)(1 -x)(beta) vertical bar x -t vertical bar(gamma), x is an element of [0, 1], t(t -1) > 0, alpha > -1, beta >-1, gamma is an element of R. As is shown in [D. Dai and L. Zhang, Painleve VI and Henkel determinants for the generalized Jocobi weight, J. Phys. A: Math. Theor. 43 (2010), Article ID: 055207, 14pp.], the corresponding Hankel determinant is the t-function of a particular Painleve VI. We present all the possible asymptotic expansions of the solution of the Painleve VI equation near 0, 8 and 1 for generic (alpha, beta, gamma). For four special cases of (alpha, beta, gamma) which are related to the dimension of the Hankel determinant, we can find the exceptional solutions of the Painleve VI equation according to the results of [A. Eremenko, A. Gabrielov and A. Hinkkanen, Exceptional solutions to the Painleve VI equation, preprint (2016), arXiv: 1602.04694], and thus give another characterization of the Hankel determinant.