General Mathematics, Vol. 4, 1996
Abstract: In the book entitled "Methodus differentialis" published in 1711, Newton indicates in the cases $m\in \{5,6\}$, without proofs, new formulas for his interpolation polynomial $N_{m}$ introduced in 1687. Arnold Kowalewski [1] has proved these formulas only in these particular cases. Slight modifications of these proofs are published in 1932 by Gerhard Kowalewski [2]. At the same time, in [2] it is shown that the new formulas are more efficient in the computation than the original formula of Isaac Newton. The aim of this paper is to establish the interpolation formulas indicated in particular cases by A. and G. Kowalewski brothers, for an arbitrary $m$.
Classification (MSC91): 41A05
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