Stirling interpolation formula

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The half-sum of the Gauss interpolation formula for forward interpolation with respect to the nodes at the point :

and Gauss' formula of the same order for backward interpolation with respect to the nodes :

Using the notation

Stirling's interpolation formula takes the form:

For small , Stirling's interpolation formula is more exact than other interpolation formulas.


[1] I.S. Berezin, N.P. Zhidkov, "Computing methods" , Pergamon (1973) (Translated from Russian)


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


[a1] F.B. Hildebrand, "Introduction to numerical analysis" , Dover, reprint (1987) pp. 139
How to Cite This Entry:
Stirling 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