In mathematics, an ultrapolynomial is a power series in several variables whose coefficients are bounded in some specific sense.
Definition.
Let formula_1 and formula_2 a field (typically formula_3 or formula_4) equipped with a norm (typically the absolute value). Then a function formula_5 of the form formula_6 is called an ultrapolynomial of class formula_7, if the coefficients formula_8 satisfy formula_9 for all formula_10, for some formula_11 and formula_12 (resp. for every formula_11 and some formula_14).
References.
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