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The use of associated Legendre polynomials for interpolation

Published online by Cambridge University Press:  24 October 2008

E. L. Albasiny
E. L. Albasiny
Affiliation:
The National Physical Laboratory Teddington
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Abstract

Several writers have dealt with the use of Chebyshev polynomials as aids to interpolation. The present paper considers the theory with associated Legendre polynomials replacing those of Chebyshev. Interpolation formulae of both Bessel and Everett type are derived, and formulae and expansions are given for evaluating the coefficients required in them either directly or in terms of derivatives or central differences. The introduction summarizes a number of formulae for polynomial interpolation and indicates the relationship between the new formulae and the old.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 2 , April 1961 , pp. 288 - 303
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Clenshaw, C. W., The numerical solution of linear differential equations in Chebyshev series. Proc. Camb. Phil. Soc. 53 (1957), 134–49.CrossRefGoogle Scholar
(2)Clenshaw, C. W., and Olver, F. W. J., The use of economized polynomials in mathematical tables. Proc. Camb. Phil. Soc. 51 (1955), 614–28.CrossRefGoogle Scholar
(3)Fox, L., The use and construction of mathematical tables. N.P.L. Mathematical Tables 1. (H.M. Stationery Office, 1956.)Google Scholar
(4)Hartree, D. R., Numerical analysis (Oxford, 1952).Google Scholar
(5)Interpolation and allied tables. (H.M. Stationery Office, 1936.)Google Scholar
(6)Interpolation and allied tables. (H.M. Stationery Office, 1956.)Google Scholar
(7)Kopal, Z., Numerical analysis. (London, 1955.)Google Scholar
(8)Magnus, W., and Oberhettinger, F., Special functions of mathematical physics. (New York, 1949.)Google Scholar
(9)Miller, J. C. P., Two numerical applications of Chebyshev polynomials. Proc. Roy. Soc. Edinb. Sect. A, 62 (1943–1949), 204–10.Google Scholar
(10)Watson, G. N., Theory of Bessel functions. (Cambridge, 1944.)Google Scholar