content_image/320672.jpg content_image/320673.jpg content_image/320676.jpg content_image/320674.jpg
such a function to the sum rule is given by 

<img src='content_image/320672.jpg'>

which is independent of the continuum threshold s$_{0}$ . The following result is useful in order to calculate the Borel transform [97]: 

<img src='content_image/320673.jpg'>

Note that Eq. (1.89) can be extended to cases where the denominator is raised to a higher power by differentiating with respect to t$_{0}$ . 

<img src='content_image/320676.jpg'>

Functions that have a branch cut can be dealt with using the relationship between the Borel transform and the inverse Laplace transform (1.82). The contribution to the sum rule is given by 

<img src='content_image/320674.jpg'>

