Skip to main content

Euler’s contribution to cardinal spline interpolation: The exponential Euler splines

  • Chapter
Leonhard Euler 1707–1783

Abstract

In my monograph [8] of 1973, dedicated to Euler, I already discussed the subjects of the title. On the occasion of the bicentenial of Leonhard Euler we present here an outline of these results, which seem to fit well in what we think of as Eulerian Mathematics.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Carlitz, L., Eulerian numbers and polynomials, Mathematics Magazine 33, 1959, p.247–260.

    Article  Google Scholar 

  2. Euler, L., Institutiones calculi differentialis, vol. II, 1755 (E. 212/O. I, 10).

    Google Scholar 

  3. Goodman, T. N. T., Schoenberg, I. J., Sharma, A., High order continuity implies good approximations to solutions of certain functional equations, submitted to Comment. Math. Helvet.

    Google Scholar 

  4. Greville, T. N. E., Schoenberg, I. J., Sharma, A., The behavior of the exponential Euler spline S n (x; t) as n→∞ for negative values of the base t, to be submitted for publication.

    Google Scholar 

  5. Hart, J. F., et al., Computer Approximations, John Wiley, New York 1968.

    MATH  Google Scholar 

  6. Norlund, N. E., Vorlesungen über Differenzenrechnung, Springer, Berlin 1924.

    Google Scholar 

  7. Schoenberg, I. J., Cardinal interpolation and spline functions IV. The exponential Euler splines, ISNM 20, 1972, p. 382–404, Birkhauser Verlag.

    Google Scholar 

  8. Schoenberg, I.J., Cardinal spline interpolation, CBMS Monograph No. 12, 1973, SIAM, Philadelphia, Pa.

    Google Scholar 

  9. Schoenberg, I. J., The elementary cases of Landau’s problem of inequalities between derivatives, Amer. Math. Monthly 80, 1973, p. 121–148.

    Article  MATH  MathSciNet  Google Scholar 

  10. Schoenberg, I. J., A new approach to Euler splines, to appear in Journal of Approximation Theory.

    Google Scholar 

  11. Subbotin, J. N., On the relations between finite differences and the corresponding derivatives, Proc. Steklov Inst. Math. 78. 1965, p. 24–42; Amer. Math. Soc. Transl., 1967, p. 23–42.

    MATH  MathSciNet  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Birkhäuser Verlag, Basel · Boston · Stuttgart

About this chapter

Cite this chapter

Schoenberg, I.J. (1983). Euler’s contribution to cardinal spline interpolation: The exponential Euler splines. In: Leonhard Euler 1707–1783. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9350-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-9350-3_9

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9351-0

  • Online ISBN: 978-3-0348-9350-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics