Research Article

On Infinite Series and with Their Some Applications to Euler's Summation Formula

Abdel Radi Abdel Gadir Abdel Rahman
Omdurman Islamic University, Sudan
* Corresponding author
Neama Yahia Mohammed
Tabuk University, Saudi Arabia
Subhi Abdalazim Aljily
University of AL Butana, Sudan
Nidal Elamen Mohammed Ali
Omdurman Islamic University, Sudan
DOI icon 10.24018/ejmath.2021.2.3.32

Read Counter
1008

Downloads
440

Citations

Share

Article Sidebar

Submitted 2021-03-23
Published 2021-07-05

Read counter = 1008 times

Table of Contents

Article Main Content

Infinite series is still used in engineering, mathematical and physical sciences.In the modern area a great progress is made in the sciences of calculus in addition to what was accompanied by advances in infinite series and their some applications .The aims of this paper is to develop and introduces the infinite series and their some applications to Euler's summation , also we show and explain how to apply the infinite series in Euler's summation .We followed the induction mathematical method and found that : The relationship through the Euler's summation focused on the physical link questioner to make the study as an application for Euler's summation so it can be the beginning of advanced study in concept of the infinite series and their some applications to Euler's summation.

Keywords: Applications, Euler's Summation Formula, Infinite Series

References

  1. E T. Whittaker, M, A- A course of Modern Analysis -London. -1902.
     Google Scholar
  2. DR. Konrad Knopp - Theory and Application of Infinite Series-Fourth German Edition, 1951.
     Google Scholar
  3. H.S. Carslaw - Introduction to the Theory of Fourier's Series and Integrals-Second Edition Llondon-1921.
     Google Scholar
  4. James. M. Hysiop -Infinite Series-New York-1959.
     Google Scholar
  5. James Nearing- Mathematical Tools for Physics- Copyright 2003.
     Google Scholar
  6. John Wiley &Sons –Calculus Volume II -Second Edition –London -copyright 1962.
     Google Scholar
  7. Malcolm R. Adams -Sequences and Series and Introduction to Mathematical Analysis 2007.
     Google Scholar
  8. Maria Predoi - Mathematical Analysis Vol. II Integral Calculus 2005.
     Google Scholar
  9. Michael Corral -Vector Calculus- Copyright 2008.
     Google Scholar
  10. Omar Hijab -Introduction to Calculus and Classical Analysis-Second Edition-2007.
     Google Scholar
  11. R. B. Dingle- Asymptotic Expansions Their Derivation and Interpretation- Acndemic Press Inc-London- Copyright 1973.
     Google Scholar
  12. Robert Wrede, Ph. D.Murrayr. Spiegel, Ph.D. -Theory and Problems of Advanced Calculus-Second Edition-Schaum’s Outline Series-New York-Copyright 2002, 1963 by The McGraw-Hill Companies.
     Google Scholar
  13. Sean- Introduction to Methods of Applied Mathematics-Anti-Copyright 1995-2001- Mauch Publishing Company-January 24, 2004.
     Google Scholar
  14. Sever Angel Popescu - Mathematical Analysis Integral Calculus - Bucharest-February, 2011.
     Google Scholar
  15. Thaddeus H. Black- Derivations of Applied Mathematics-Copyright 1983-2012.
     Google Scholar
  16. T.J. PA. Bromwh'h. M.A- An Introduction to the Theory of Infinite Series - London 1908.
     Google Scholar
  17. William F. Trench- Introduction to Real Analysis -Texas, Free Edition- 24 December 2013.
     Google Scholar