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XXII.—Two Numerical Applications of Chebyshev Polynomials

Published online by Cambridge University Press:  14 February 2012

J. C. P. Miller
J. C. P. Miller
Affiliation:
University of Liverpool.
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Extract

In this paper two computational processes are outlined in which the table of Chebyshev Polynomials Cn(x) = 2 cos (n cos−1 ½x) given in the preceding paper may be used with effect; these processes are (a) interpolation and (b) Fourier synthesis. A brief outline is also given of the idea behind the process of “Economization of Power Series” developed in Lanczos, 1938; this is related to (a). Finally the application of (b) to the calculation of Mathieu functions is considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 62 , Issue 2 , 1946 , pp. 204 - 210
Copyright
Copyright © Royal Society of Edinburgh 1946

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References

REFERENCES TO LITERATURE

Comrie, L. J., 1936. Interpolation and Allied Tables. Reprinted from Nautical Almanac for 1937, and issued separately. Revised reprint, 1942. H.M. Stationery Office, London.Google Scholar
Ince, E. L., 1932. “Tables of the Elliptic Cylinder Functions,” Proc. Roy. Soc. Edin., LII, 355–423.Google Scholar
Lanczos, C., 1938. “Trigonometric Interpolation of Empirical and Analytical Functions,” Journ. Math. Phys., XVII, 123–199.CrossRefGoogle Scholar
Oppolzer, T. R. Von, 1880. Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Zweiter Band, Engelmann, Leipzig.Google Scholar
Stratton, J. A., Morse, P. M., Chu, L. J., and Hutner, R. A., 1941. Elliptic Cylinder and Spheroidal Wave Functions, including Tables of Separation Constants and Coefficients. (Pages 1-51 are reprinted from Journ. Math. Phys., XX, 259-309.) Wiley, New York; Chapman and Hall, London.Google Scholar
Van der Pol, B., and Weijers, T. J., 1933. “Tchebycheff Polynomials and their Relation to Circular Functions, Besselfunctions and Lissajous-Figures,” Physica, 1, No. 1, 78–96.CrossRefGoogle Scholar
Watson, G. N., 1922. A Treatise on the Theory of Bessel Functions, Cambridge University Press.Google Scholar