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XXI.—Tables of Chebyshev Polynomials

Published online by Cambridge University Press:  14 February 2012

C. W. Jones ,
J. C. P. Miller ,
J. F. C. Conn  and
R. C. Pankhurst
C. W. Jones
Affiliation:
University of Liverpool
J. C. P. Miller
Affiliation:
University of Liverpool
J. F. C. Conn
Affiliation:
National Physical Laboratory
R. C. Pankhurst
Affiliation:
National Physical Laboratory
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Extract

1. Introduction.—The object of this paper is twofold: firstly, to present a table of the Chebyshev polynomials Cn(x) = 2 cos (n cos−1 ½x) for n = I(I)12 and x = o(o·o2)2, values being exact or to 10 decimals; secondly, to provide a working list of coefficients and formulæ relating to these and allied functions.

Valuable accounts of applications and properties will be found in Van der Pol and Weijers, 1933, in Lanczos, 1938, and in Szego, 1939. Further applications are indicated in the following paper, by J. C. P. Miller, which also suggests methods of reducing the inconvenience caused by the present lack of tables of the allied polynomials Sn(x). It is hoped that suitable tables will be prepared later.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 62 , Issue 2 , 1946 , pp. 187 - 203
Copyright
Copyright © Royal Society of Edinburgh 1946

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References

REFERENCES TO LITERATURE

Lanczos, C., 1938. “Trigonometric Interpolation of Empirical and Analytical Functions”, Journ. of Math, and Phys., XVII, 123–199.CrossRefGoogle Scholar
Szegö, G., 1939. Orthogonal Polynomials, Amer. Math. Soc, New York.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