An Infinite Order Whittaker Function In this paper we construct a flat smooth section of an induced space $I(s,\eta)$ of $SL_2(\mathbb{R})$ so that the attached Whittaker function is not of finite order. An asymptotic method of classical analysis is used. Categories:11F70, 22E45, 41A60, 11M99, 30D15, 33C15