Formal Summation of Divergent Series

@article{Dawson1998FormalSO,
  title={Formal Summation of Divergent Series},
  author={Robert J. MacG. Dawson},
  journal={Journal of Mathematical Analysis and Applications},
  year={1998},
  volume={225},
  pages={532-541}
}
  • R. Dawson
  • Published 15 September 1998
  • Physics
  • Journal of Mathematical Analysis and Applications
The idea of telescoping a series is widely known, but is not widely trusted. It is often treated as a formalism with no meaning, unless convergence is already established. It is shown here that even for divergent series, the results of telescoping are self-consistent, and consistent with other well-behaved summation operations. Moreover, the summation operations obtained by telescoping are the strongest possible operations with these properties. Some Tauberian theorems are exhibited for… 
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