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Formally, a function <math>f</math> is ''real analytic'' on an [[open set]] <math>D</math> in the [[real line]] if for any <math>x_0\in D</math> one can write
:<math>
f(x) = \sum_{n=0}^\infty a_{n} \left( x-x_0 \right)^{n} = a_0 + a_1 (x-x_0) + a_2 (x-x_0)^2 + a_3 (x-x_0)^3 + \cdots
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