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XXIV.—The General Form of the Orthogonal Polynomials for Simple Series, with Proofs of their Simple Properties

Published online by Cambridge University Press:  15 September 2014

F. E. Allan
F. E. Allan
Affiliation:
Statistical Department, Rothamsted Experimental Station, Harpenden, Herts
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Extract

In Statistical Methods for Research Workers R. A. Fisher (1) has given a numerical method of curve fitting by means of orthogonal polynomials. It is proposed here to show how the properties of these polynomials and a general formula for them may be developed from the properties of their terminal differences, thus providing general proofs of the properties utilised in the numerical method.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 50 , 1931 , pp. 310 - 320
Copyright
Copyright © Royal Society of Edinburgh 1931

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References

REFERENCES

(1)Fisher, R. A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver & Boyd. (3rd. ed. 1930.)Google Scholar
(2)Tchebycheff, P. L. (1854 to 1875). See Œuvres (1899), tome 1.Google Scholar
(3)Esscher, F. (1920). Über die Sterblichkeit in Schweden (1886 to 1914), Lunds Astronomiska Observatorium.Google Scholar
(4)Fisher, R. A. (1921). “Studies in Crop Variation.—I. An Examination of the Yield of Dressed Grain from Broadbalk,” Jour. Agric. Sci., vol. xi, pp. 107–135.CrossRefGoogle Scholar
(5)Jordan, C. (1921). Proc. Lond. Math. Soc., Ser. 2, vol. xx, pp. 297–325.Google Scholar