Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-25T14:39:10.613Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Properties of a Certain set of Interpolating Polynomials

Published online by Cambridge University Press:  20 November 2018

David J. Leeming
David J. Leeming*
Affiliation:
Department of Mathematics, University of Victoria, VictoriaBritish ColumbiaCanada
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A Lidstone series provides a (formal) two-point expansion of a given function f(x) in terms of its derivatives of even order at the nodes 0 and 1 and takes the form.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 4 , October 1975 , pp. 529 - 537
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Al-Salaam, W. and Verma, A., Generalized Sheffer polynomials, Duke Math. J. 37 (1970), 361–365.Google Scholar
2. Carlitz, L., Note on the coefficients of cosh x/cos x, Mathematics Magazine, 32 (1955), 132 and 136.Google Scholar
3. Carlitz, L., The Coefficients o/cosh x/cos x, Monatshefte fur Mathematik, 69 (1965), 129–135.Google Scholar
4. Leeming, D. J., A generalization of completely convex functions and related problems, Ph.D. Thesis, 1969.Google Scholar
5. Norlund, N. E., Vorlesungen uber Differenzenrechnung, Chelsea, New York, 1954.Google Scholar
6. Osegov, V. B., Some extremal properties of generalized Appell polynomials, Soviet Maths. 5 (1964), 1651–1653.Google Scholar
7. Pethe, S. P. and Sharma, A., Modified Abel expansion and a subclass of completely convex functions, SIAM J. Math. Anal., 3 (1972), 546–558.Google Scholar
8. Ryser, H. J., Combinatorial Mathematics, published by The Mathematical Association of America, distributed by John Wiley and Sons, Inc., New York, 1963.Google Scholar
9. Schoenberg, I. J., On certain two point expansions of integral functions of exponential type, Bull. Amer. Math. Soc, 42 (1936), 284–288.Google Scholar
10. Whittaker, J. M., On Lidstone series and two point expansions of analytic functions, Proc. London Math. Soc, 36 (1934), 451–469.Google Scholar
11. Widder, D. V., Completely convex functions and Lidstone series, Trans. Amer. Math. Soc. 51 (1942), 387–398.Google Scholar