Analytic function: Difference between revisions

Revision as of 14:35, 23 December 2020

Revision as of 22:42, 13 January 2021

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in which the coefficients <math>a_0, a_1, \dots</math> are real numbers and the [[series (mathematics)|series]] is [[convergent series|convergent]] to <math>f(x)</math> for <math>x</math> in a neighborhood of <math>x_0</math>.

Alternatively, ana real analytic function is an [[smooth function|infinitely differentiable function]] such that the [[Taylor series]] at any point <math>x_0</math> in its ___domain

:<math> T(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(x_0)}{n!} (x-x_0)^{n}</math>