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One of the most commonly used methods for deriving formulas for bivariate interpolation is that of extending to two variables the formulas of Lagrange, Aitken, Newton, Gauss, Stirling, Everett, Bessel, etc., in which forward, backward and central-differences are used. These formulas have the property that the resulting interpolation polynomial agrees with the interpolated function, fix, y), at each of the node points of a Cartesian grid. In this study, we shall investigate the existence of adoi:10.2307/2003300 fatcat:zvxkb47x45fg7dck2xftwwtdpq