Steffensen interpolation formula

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A form of notation of the interpolation polynomial obtained from the Stirling interpolation formula by means of the nodes at a point :

using the relations

After collecting similar terms, the Steffensen interpolation formula can be written in the form


[1] G.A. Korn, T.M. Korn, "Mathematical handbook for scientists and engineers" , McGraw-Hill (1968)


The central differences , ( ) are defined recursively from the (tabulated values) by the formulas

The Steffensen interpolation formula is also known as Everett's second formula.


[a1] F.B. Hildebrand, "Introduction to numerical analysis" , McGraw-Hill (1956) pp. 103–105
[a2] J.F. Steffensen, "Interpolation" , Chelsea, reprint (1950)
[a3] C.-E. Froberg, "Introduction to numerical analysis" , Addison-Wesley (1965) pp. 157
How to Cite This Entry:
Steffensen interpolation formula. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.K. Samarin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article