【摘 要】
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In this work,we give the asymptotic characterization of the Hankel determinant as n tends to in_nity,and this Hankel determinant generated from a Pollaczek-
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In this work,we give the asymptotic characterization of the Hankel determinant as n tends to in_nity,and this Hankel determinant generated from a Pollaczek-Jacobi type weigh as $$w(x; t)= x^{\alpla}(1-x)^{beta}e^{-t/x}},x\in [0,1],t\geq 0,\beta>0,\alpha>0$$ first studied by Chen and Dai.In order to give the asymptotic expression of this Hankel determinant,we introduce a scale scheme and derived that the logarithmic derivative of the Hankel determinant satisfies a $\rho$-from Painleve equation which associates with the Hamiltionian in the Okamotos development of the Painlev_e equation and we also derive a particular Painlev_e equation PIII(1;2$\alpha$; 0;1).Moreover,this Painleve equations are stable for large $\beta$.
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