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Extension of Summation Formulas involving Stirling series

Number Theory 2016-05-31 v1

Abstract

This paper presents a family of rapidly convergent summation formulas for various finite sums of the form k=0xf(k)\sum_{k=0}^{\lfloor x\rfloor}f(k), where xx is a positive real number.

Keywords

Cite

@article{arxiv.1605.09204,
  title  = {Extension of Summation Formulas involving Stirling series},
  author = {Raphael Schumacher},
  journal= {arXiv preprint arXiv:1605.09204},
  year   = {2016}
}