Various algorithms have been proposed to solve the interconversion equation of linear viscoelasticity when Prony series are used for the relaxation and creep moduli, G(t) and J(t). With respect to a Prony series for G(t), the key step in recovering the corresponding Prony series for J(t) is the determination of the coefficients {j(k)} of terms in J(t). Here, the need to solve a poorly conditioned matrix equation for the {j(k)} is circumvented by deriving elementary and easily evaluated analytic formulae for the {j(k)} in terms of the derivative d (G) over cap (s)/ds of the Laplace transform (G) over cap (s) of G(t). (C) 2015 The Society of Rheology.