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On a New Interpolation Formula

Published online by Cambridge University Press:  18 August 2016

J. D. Everett
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Extract

The two leading formulæ at present in use for interpolation by central differences are due to Newton‡ (Methodus Differentialis, Prop. III), though often called by the name of Stirling, who republished them about 20 years later.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 35 , Issue 6 , January 1901 , pp. 452 - 458
Copyright
Copyright © Institute and Faculty of Actuaries 1900

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References

* Hor. Carm. iii, 30, Ad Melpomenen.

† Newton also invented the common formula in advancing differences, in which the coefficients are those of the binomial theorem. He gives it in Lemma 5, which follows Prop. 40 of Book 3 of the Principia; but its identity i s veiled by a geometrical disguise, rendered thicker by reversal of sign in the definition of Δ.