In this work a new form of functional interpolation is introduced, dubbed plateau function interpolation. As per usual, an approximating function is synthesised as a linear combination of simple well-known functions. But here, the simple functions need not be taken from a single class of functions.

The interpolation scheme enables known qualitative behaviour of the function of interest to be exploited easily and efficiently. For example, the trigonometrics, exponentials and rationals may easily be combined in a single interpolation to capture periodic, secular and asymptotic behaviour, respectively, over different parts of the domain interval.

The interpolation scheme is amenable to analytical work because it enables a single closed-form expression of the synthesised function to be calculated. And the expression is usually C^∞–continuous over the entire domain interval, not piecewise continuous over contiguous sub-intervals.

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