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regular singularities by using their Fredholm determinant representation [8], and show that they. ... using the Fredholm determinant, and H.D thanks Andrei Prokhorov for numerous discussions.

2πi. C. R(λ′′,λ′). λ′′ λdλ′′ dλ̄′′. Recall (see, for example [79]) that the Fredholm determinant D is defined by the series. ... We found also the meaning of the τ-function of the Hirota–Miwa equation for thatclass of

Then one can express the determinant on the righthand side of (20) as the exponential e. ... dµ(w). In order to manipulate the regularized Fredholm determinant we approximate the right handside by.

18] formula of Fredholm type:. u(x,t) =22x ln det [1N G(x,t)] , where. ... CCme. iπ(ψψm). ],mS. (2.52). This last summation is precisely the Fredholm expansion of the determinant [23] in the statement.