Abstract

Let \=\Sigma _{k\ge 0}a_{k}z^{k}\) be a transcendental entire function with real coefficients. The main purpose of this paper is to show that the restriction of f to \ is not definable in the ordered field of real numbers with restricted analytic functions, \. Furthermore, we show that there is \ such that the function \\) on \ is not definable in \, where \ the expansion of the real field generated by multisummable real series.