  The diagonal spin-spin correlations of the square lattice Ising model,
originally expressed as Toeplitz determinants, are given by two distinct
Fredholm determinants - one with an integral operator having an Appell function
kernel and another with a summation operator having a Gauss hypergeometric
function kernel. Either determinant allows for a Neumann expansion possessing a
natural \lambda - parameter generalisation and we prove that both expansions
are in fact equal, implying a continuous and a discrete representation of the
form factors. Our proof employs an extension of the classic study by Geronimo
and Case, applying scattering theory to orthogonal polynomial systems on the
unit circle, to the bi-orthogonal situation.
