Methods for the evaluation of divergent series

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  • This is an expository thesis, which reviews the recent work of Agnew, Vuckovic, Martic and Jakimovski on the Lototsky summability method and its generalisations. An introductory sketch of summability theory is provided, and it is noted that a more general form of the Lototsky method was already introduced by Karamata In 1935. In reviewing the recent work some minor errors are corrected, and details of proofs, or in some cases entire proofs, are supplied. In particular, the theorem stated by Martic, that the Karamata method includes the Euler, is proved in detail. Part of the work is clarified by the use of finite difference theory (Stirling's numbers), and some other simplifications are made.

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  • Copyright ¬© 1963 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
Date Created
  • 1963


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