A uniformly convergent alternative to the davidson-cole distribution function

Abstract

A new skewed-arc alternative to the Davidson-Cole permittivity function is derived. It has the same very low and very high frequency limit angles in its Cole-Cole arc and approaches the behavior of the Davidson-Cole permittivity function for small values of the exponent parameter β. The difference, however, becomes increasingly appreciable for large values of β. The distribution function g(ln τ) is very much like that for the Davidson-Cole system, but it does not exhibit any singular nor discontinuous slope behavior for any value of the relaxation time τ.