# Stirling interpolation formula

From Encyclopedia of Mathematics

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.

#### References

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

#### Comments

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

#### References

[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: http://encyclopediaofmath.org/index.php?title=Stirling_interpolation_formula&oldid=12181

This article was adapted from an original article by M.K. Samarin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article