On the Solution of a Painlevé III Equation
نویسنده
چکیده
In a 1977 paper of McCoy, Tracy and Wu [2] there appeared for the first time the solution of a Painlevé equation in terms of Fredholm determinants of integral operators. Specifically, it was shown that a one-parameter family of solutions of the equation ψ ′′ (t) + t −1 ψ ′ (t) = 1 2 sinh 2ψ + 2α t −1 sinh ψ, (1) a special case of the Painlevé III equation, is given by ψ(t) =
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