From (10), the distribution of excitation on the cortical plane can be explicitly rewritten as

where, see equations (9) and (11)

According to the method of Fredholm for inhomogeneous integral equations [121] an approximate solution of equation (18) can be expressed in the form

where

Substituting from (19) and comparing the result with (8) we identify the kernel and thence the resulting RF after recurrent inhibition:

Making explicit the parametric mapping between cortical plane (**C**) and
visual field (**S**), the resulting RF can be formulated as

where

is the * equivalent inhibitory kernel in the feed-forward form*.
denotes the Jacobian
of and the absolute value of its determinant is the local
magnification factor of the mapping .
A more detailed derivation of this solution can be found in the Appendix.