An approximate solution of (18) can be expressed in the form

where and are
respectively the Fredholm determinant and the Fredholm first minor of the
kernel and are expressible as power series in **b**
[121]:

The coefficients can be computed by using the following relations [82]

Substituting from (19) and comparing the result with (8) we identify the kernel of an equivalent feed-forward operator

The application of parametric mapping leads to

where , being the Jacobian of the transformation .