Cauchy’s Cours d’analyse pp 59-70 | Cite as

# Determination of integer functions, when a certain number of particular values are known. Applications.

[83] To determine a function when a certain number of particular values are taken to be known is what we call to *interpolate*. When it is a matter of a function of one or two variables, this function can be considered as the ordinates of a curve or of a surface, and the problem of *interpolation* consists of fixing the general value of this ordinate given a certain number of particular values, that is to say, to make the curve or the surface pass through a certain number of points. This question can be solved in an infinity of ways, and in general the problem of interpolation is indeterminate. However, the indeterminacy will cease if, to the knowledge of the particular values of the desired function, we add the expressed condition that this function be integer, and of a degree such that the number of its terms becomes precisely equal to the number of particular values given.

## Keywords

Single Variable Ordinate Variable Surface Pass Lagrange Interpolation Typographical Error## Preview

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