Skip to main content
SpringerLink
Log in

Modified Equations and the Basel Problem

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Martin Aigner and Günter M. Ziegler. Proofs from THE BOOK. 5th edition, Springer, Berlin, 2014.

  • Jonathan M. Borwein and Peter B. Borwein. Pi and the AGM. Wiley, New York, 1987.

  • Robin Chapman. Evaluating \(\zeta (2)\). Preprint, http://empslocal.ex.ac.uk/people/staff/rjchapma/etc/zeta2.pdf, 1999.

  • William Dunham. Euler: The Master of Us All. The Mathematical Association of America, Washington, 1999.

  • Ernst Hairer, Christian Lubich, and Gerhard Wanner. Geometric Numerical Integration Illustrated by the Störmer-Verlet Method. Acta Numerica, 12(12):399–450, 2003.

  • Ernst Hairer, Christian Lubich, and Gerhard Wanner. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. Springer, Berlin, 2006.

  • Ishtiaq Rasool Khan, Ryoji Ohba, and Noriyuki Hozumi. Mathematical Proof of Closed Form Expressions for Finite Difference Approximations Based on Taylor Series. J. Comput. Appl. Math., 150(2):303–309, 2003.

  • Konrad Knopp. Theory and Application of Infinite Series. Blackie & Son Limited, London, 1954.

  • Mats Vermeeren. Modified Equations for Variational Integrators. Numer. Math., 137(4):1001–1037, 2017.

Download references

Acknowledgments

The author is grateful to the numerous people who gave constructive criticism on some draft of this work, in particular Yuri Suris and the anonymous referees. The author is supported by the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics.”

Author information

Authors and Affiliations

  1. Institut für Mathematik, MA 7-1, Technische Universität Berlin Str. des 17. Juni 136, 10623, Berlin, Germany

    Mats Vermeeren

Authors
  1. Mats Vermeeren
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mats Vermeeren.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vermeeren, M. Modified Equations and the Basel Problem. Math Intelligencer 40, 33–37 (2018). https://doi.org/10.1007/s00283-017-9767-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00283-017-9767-1

Search

Navigation