An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions

@article{Vepstas2007AnEA,
  title={An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions},
  author={Linas Vepstas},
  journal={Numerical Algorithms},
  year={2007},
  volume={47},
  pages={211-252}
}
  • L. Vepstas
  • Published 9 February 2007
  • Mathematics
  • Numerical Algorithms
This paper sketches a technique for improving the rate of convergence of a general oscillatory sequence, and then applies this series acceleration algorithm to the polylogarithm and the Hurwitz zeta function. As such, it may be taken as an extension of the techniques given by Borwein’s “An efficient algorithm for computing the Riemann zeta function” by Borwein for computing the Riemann zeta function, to more general series. The algorithm provides a rapid means of evaluating Lis(z) for general… 
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