Discussion on answer by Calvin Khor: Solution for Cauchy Problem $u_t-u_{xx} = 0$ belongs to the Gevrey class of order $1/2$

Imported from a comment discussion on https://math.stackexchange.com/questions/3018750/solution-for-cauchy-problem-u-t-u-xx-0-belongs-to-the-gevrey-class-of-orde/3021619#3021619