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MotivationThere are a lot of nice properties of analytic functions, whose class is denoted by $C^\omega$. Formally we have the following definition:If $f \in C^\omega$ and $x_0 \in \mathbb{R}$, one can writef = a_0+a_1(x-x_0)+a_2(x-x_0)^2+\cdots.Obviously $f \in C^\infty$ (and hence $C^\omega \subset C^\infty$) and alternatively we have the Taylor series converges to $f$ for any $x_0 \in \mathbb{R}$:T(x) = \sum_{n=0}^{\infty}\frac{D^nf(x_0)}{n!}(x-x_0)^n.One interesting thing is, every $f \in C^...