A Fredholm integral equation of the first kind is an integral equation of the form
 |
(1)
|
where 
is the kernel and 
is an unknown function to be solved for (Arfken 1985,
p. 865).
If the kernel is of the special form 
and the limits are infinite so that the equation becomes
 |
(2)
|
then the solution (assuming the relevant transforms exist) is given by
)/(F_x[K(x)](k))e^(2piikx)dk,](/images/equations/FredholmIntegralEquationoftheFirstKind/NumberedEquation3.svg) |
(3)
|
where 
is the Fourier transforms
operator (Arfken 1985, pp. 875 and 877).
