Preprints of the Keldysh Institute of Applied Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Keldysh Institute preprints:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Preprints of the Keldysh Institute of Applied Mathematics, 2022, 028, 23 pp.
DOI: https://doi.org/10.20948/prepr-2022-28
(Mi ipmp3054)
 

This article is cited in 4 scientific papers (total in 4 papers)

Functional summation of series

V. P. Varin
Full-text PDF (329 kB) Citations (4)
References:
Abstract: We consider a summation technique which reduces summation of a series to the solution of some linear functional equations. Partial sums of a series satisfy an obvious difference equation. This equation is transformed to the functional equation on the interval $[0,1]$ for the continuous argument. Then this equation is either solved explicitly (to within an arbitrary constant) or an asymptotic expansion of the solution is computed at the origin. The sum of the original series is determined uniquely as a constant needed for the matching of the asymptotic series with partial sums of the original series. The notion of a limit is not involved in this computational technique, which allows summation of divergent series as well.
Keywords: summation of series, functional equations, divergent series.
Document Type: Preprint
UDC: 521.1+531.314
Language: Russian
Citation: V. P. Varin, “Functional summation of series”, Keldysh Institute preprints, 2022, 028, 23 pp.
Citation in format AMSBIB
\Bibitem{Var22}
\by V.~P.~Varin
\paper Functional summation of series
\jour Keldysh Institute preprints
\yr 2022
\papernumber 028
\totalpages 23
\mathnet{http://mi.mathnet.ru/ipmp3054}
\crossref{https://doi.org/10.20948/prepr-2022-28}
Linking options:
  • https://www.mathnet.ru/eng/ipmp3054
  • https://www.mathnet.ru/eng/ipmp/y2022/p28
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Препринты Института прикладной математики им. М. В. Келдыша РАН
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024