Convergence Acceleration Techniques
  This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the acceleration of slowly convergent and the summation of divergent series that are ubiquitous in relevant applications. The computing time is reduced in many cases by orders of magnitude. 
U. D. Jentschura, S. V. Aksenov, P. J. Mohr, M. A. Savageau, and G.   Soff