The -method and Fredholm integral equations

Instead of using approximate methods on the equation

$\text{f(x) = g(x) + λ}\text{∫}\text{0}\text{1}\text{K(x,t)f(t) dt}$

, the τ-method is employed to obtain the exact solution of the equation

$\text{h(x) = g(x) + λ}\text{∫}\text{0}\text{1}\text{K(x,t)h(t) dt + R(x,λ)}$

,The analytical from of R(x, λ) determines the type of approximation which results. In this paper R(x, λ) is chosen to be a function which is rational in the parameter λ in which case, the approximation to the true solution has the same character. An example is given.