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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Carlitz, L., Eulerian numbers and polynomials, Mathematics Magazine 33, 1959, p.247–260.
Euler, L., Institutiones calculi differentialis, vol. II, 1755 (E. 212/O. I, 10).
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.
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.
Hart, J. F., et al., Computer Approximations, John Wiley, New York 1968.
Norlund, N. E., Vorlesungen über Differenzenrechnung, Springer, Berlin 1924.
Schoenberg, I. J., Cardinal interpolation and spline functions IV. The exponential Euler splines, ISNM 20, 1972, p. 382–404, Birkhauser Verlag.
Schoenberg, I.J., Cardinal spline interpolation, CBMS Monograph No. 12, 1973, SIAM, Philadelphia, Pa.
Schoenberg, I. J., The elementary cases of Landau’s problem of inequalities between derivatives, Amer. Math. Monthly 80, 1973, p. 121–148.
Schoenberg, I. J., A new approach to Euler splines, to appear in Journal of Approximation Theory.
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.
Rights 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