  We give a review of the state of the art with regard to the theory of scale
functions for spectrally negative Levy processes. From this we introduce a
general method for generating new families of scale functions. Using this
method we introduce a new family of scale functions belonging to the Gaussian
Tempered Stable Convolution (GTSC) class. We give particular emphasis to
special cases as well as cross-referencing their analytical behaviour against
known general considerations.
