The study is motivated by a theoretical question raised by Warming and Hyett in a famous publication on the Modified Equation Approach in which they assumed the existence of a function that interpolates numerical data defined over a uniform grid, and that can be expanded, over an indefinite domain, in Taylor's series of the independent variables x and t. We establish constructively that the problem of interpolation of an arbitrary infinite sequence of data by an entire function of x (and possibly t) admits uncountabl- y many solutions. In the case of a single variable, if the data are bounded, the interpolant can be made bounded, and all its derivatives bounded. Besides, the construction is generalized to the interpolation of the values of the function and its derivatives up to an arbitrarily prescribed order (Hermitian interpolation). The proposed interpolant depends on a free parameter lambda, and its behavior as lambda varies is illustrated in a particular case by numerical experiment.