where c is a constant of integration. Consequently,

We are almost there.

To continue the analysis, we set F(x/pffi) = Jq^ D(y)dy, so that hx L expl 7— 7j{c — Fl Tffiffi.

Clearly h(0) = 0. To satisfy the other boundary condition, we must have that J*^ exp(s2/e){c — F(s/v/ë)}ds = 0 from which we conclude that exp( 7) ^ ffi d exp ( — ) ds

We now recall that D(y) ~ 1/2y for large y, so that J^^ D(y)dy ~ 1/2 log(x//e) and consequently, since the main contributions to the integrals in Eq. (8.73) come from the upper limit, we conclude c ~ 1 log(^

We keep this in mind as we proceed to the next, and final, step. Now, since F(s) > 0, from Eq. (8.72) we conclude that h(x)< -Lexp--)c exp ( — ) ds

so that

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