Resolution Of Grandi's Paradox And Investigations On Related Series


Beji S.

APPLIED MATHEMATICS E-NOTES, vol.20, pp.265-277, 2020 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20
  • Publication Date: 2020
  • Title of Journal : APPLIED MATHEMATICS E-NOTES
  • Page Numbers: pp.265-277

Abstract

Grandi's paradox is resolved by introducing a consistent truncation concept for series expansions of Grandi-type functions. In addition, a convergence improvement technique by successive averaging of truncated series of subsequent orders is presented. Resulting rectified series expansions satisfy certain critical points exactly and represent the corresponding generating functions considerably better compared to standard expansions. Finally, successive averages together with collocation technique are applied to series expansions of arbitrarily selected functions for demonstrating the improvements in series representations.