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Notes on Everett's Interpolation Formula

Published online by Cambridge University Press:  20 January 2009

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Writing of his now well-known Interpolation Formula, Professor Everett said, “The only novelty in the formula is the simplicity of its form.… The best known formulae for interpolation by central differences are difficult to carry in the memory on account of their unsymmetrical aspect, one law being applicable to the odd and another to the even terms. … This disadvantage does not apply to the formula proposed,” viz., that which now goes by Everett's name.

Research Article
Copyright © Edinburgh Mathematical Society 1921


page 21 note * Brit. Ass. Rep., 1900, p. 648.

page 21 note † Mémoire sur lea Suites; (Histoire de l'Acad. … Paris, 1779 (published 1782), pp. 217–221). The demonstration is repeated in the Théorie Anal, des Probe., p. 15–17, and is substantially reproduced in English in the Encyl-Metropolitana (Article, “Finite Differences”), Vol. II., pp. 286–7. De Morgan also gives it in his own fashion, Diff. and Int. Calc, p. 545–6.

page 22 note * Ths expansion of E n in powers of Ω would involve fractional powers, as may be seen by solving the equation

page 24 note * See Hobson's Plane Trig. (4th Ed.), p. 276, eq. (8).

page 24 note † Laplace adopted the converse process and deduced Bessel's and Stirling's formulae from his own form of Everett's, discussed supra.

page 25 note * This has been otherwise shewn by R. Todhunter, Jour. Inst Act., L., 136–7, who calls attention to the alternative method here adopted.