00185 1d0f3622615a4b0286553d665f34bf

186

McWilliams

g(hN(t);t) - g(0;t)

ai |i

}

N(t)—1

+ S J₂^l g(hj;t)(l -a2) + a^^(t) g(t;t)-a^^(t) g(hN(t);t)

j=l

{

N(t)—1

ai ^ (1 - a2) a* ₂' * g(hN(t);t) + (1 - a2) Ś a^₂ ¹ g(hj;t)

}

+ a^^(t) g(t;t) - g(0;t)

This is our finał expression for F7 _t(t). The function g(x;t) is simplified as follows.

g(x;t)

fe^Xx

1 _ -<>(t-x) y* 19(»-x)]' i=0 ^i!

dx

- I    _d.x

i=0

Substituting u = t-x in the integral

r-1 .

1 Xx ^ V 0¹ f; -$,+0)u =    e*’* + e ~t J u¹ e    du

01

i=0

Substitute: v = (X + 0)u: