Ultrapolynomial
In mathematics, an ultrapolynomial is a power series in several variables whose coefficients are bounded in some specific sense. Definition
Let  and  a field (typically  or ) equipped with a norm (typically the absolute value). Then a function  of the form  is called an ultrapolynomial of class , if the coefficients  satisfy  for all , for some  and  (resp. for every  and some ). References

Mathematical analysis