Interconversion of Prony series for relaxation and creep

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 fj k g of terms in J(t).Here, the need to solve a poorly conditioned matrix equation for the fj k g is circumvented by deriving elementary and easily evaluated analytic formulae for the fj k g in terms of the derivative d b GðsÞ=ds of the Laplace transform bGðsÞ of G(t).