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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  an approximate solution of equation (18) can be expressed in the form
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
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.