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The integrals $ I_{n}(r)$ are given in expansion around r= 0 in the basis of the formal solutions of $\\, {\\cal L}^{scal}_q$ with transcendental combination coefficients. We find that the expression $ r^{1/4}\\,\\exp(r^2/8)$ is a solution of the Painlev\\'e VI equation in the scaling limit. 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Maillard, S. Hassani","submitted_at":"2014-10-25T15:04:35Z","abstract_excerpt":"We show and give the linear differential operators ${\\cal L}^{scal}_q$ of order q= n^2/4+n+7/8+(-1)^n/8, for the integrals $I_n(r)$ which appear in the two-point correlation scaling function of Ising model $ F_{\\pm}(r)= \\lim_{scaling} {\\cal M}_{\\pm}^{-2}\n  < \\sigma_{0,0} \\, \\sigma_{M,N}> = \\sum_{n} I_{n}(r)$. The integrals $ I_{n}(r)$ are given in expansion around r= 0 in the basis of the formal solutions of $\\, {\\cal L}^{scal}_q$ with transcendental combination coefficients. We find that the expression $ r^{1/4}\\,\\exp(r^2/8)$ is a solution of the Painlev\\'e VI equation in the scaling limit. 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