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
(3)

where is the Fourier transforms operator (Arfken 1985, pp. 875 and 877).