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On Rational Approximation on the Positive Real Axis

Published online by Cambridge University Press:  20 November 2018

Q. I. Rahman  and
G. Schmeisser
Q. I. Rahman
Affiliation:
Université de Montréal, Montréal, Québec
G. Schmeisser
Affiliation:
Université de Montréal, Montréal, Québec
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Abstract

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In their study of the uniform approximation of the reciprocal of e2 by reciprocals of polynomials on the positive real axis, Cody, Meinardus, and Varga [3] showed that if denotes the class of all polynomials of degree at most n and

then

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 1 , 01 February 1977 , pp. 180 - 192
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Achieser, N. I., Theory of approximation (Frederick Ungar Publishing Co., New York, 1956).Google Scholar
2. Cheney, E. W., Introduction to approximation theory (McGraw-Hill Book Comp., New York, St. Louis, San Francisco, Toronto, London, Sydney, 1966).Google Scholar
3. Cody, W. J., Meinardus, G., and Varga, R. S., Chebyshev rational approximation to e∼x in [0, + oe) and applications to heat-conduction problems, J. Approximation Theory 2 (1969), 50–56.Google Scholar
4. Erdôs, P. and Reddy, A. R., Problems and results in rational approximation on the positive real axis, to appear, Periodica Math. Hung.Google Scholar
5. Isaacson, E. and Keller, H. B., Analysis of numerical methods (John Wiley & Sons, Inc., New York, London, Sydney, 1966).Google Scholar
6. Meinardus, G., Approximation of functions: Theory and numerical methods, Springer Tracts in Natural Philosophy Vol. 13 (Springer Verlag, Berlin, Gôttingen, New York, 1967).CrossRefGoogle Scholar
7. Polya, G. and Szegô, G., Aufgaben und Lehrsatze aus der Analysis II (Springer Verlag, Berlin, Gôttingen, Heidelberg, 1954).CrossRefGoogle Scholar
8. Schônhage, A., Zur rationalen Approximierbarkeit von e∼x iiber [0, oe), J. Approximation Theory 7 (1973), 395–398.Google Scholar
9. Specht, W., Die Lage der Nullstellen eines Polynoms IV, Math. Nachrichten 21 (1960), 201–222.Google Scholar
10. Szegô, G., Orthogonal polynomials, AMS Colloqu. Publ. Vol. XXIII (Amer. Math. Soc, New York, 1959).Google Scholar