A viscoelastic modulus admits an exact finite Prony series if and only if its Mellin kernel pole lattices align arithmetically with the constitutive integer lattice and residues satisfy decoupled first-order recurrences.
Fox, The G and H functions as symmetrical Fourier kernels, Transactions of the American Mathematical Society 98 (3) (1961) 395–429
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Mellin-Space Prony Representability of Linear Viscoelastic Models
A viscoelastic modulus admits an exact finite Prony series if and only if its Mellin kernel pole lattices align arithmetically with the constitutive integer lattice and residues satisfy decoupled first-order recurrences.