In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not hold generally for real analytic functions. A function is analytic if and only if it is equal to its Taylor series in some neighborhood of every point.
Read more about Analytic Function: Definitions, Examples, Alternate Characterizations, Properties of Analytic Functions, Analyticity and Differentiability, Real Versus Complex Analytic Functions, Analytic Functions of Several Variables
Famous quotes containing the words analytic and/or function:
““You, that have not lived in thought but deed,
Can have the purity of a natural force,
But I, whose virtues are the definitions
Of the analytic mind, can neither close
The eye of the mind nor keep my tongue from speech.””
—William Butler Yeats (1865–1939)
“It is not the function of our Government to keep the citizen from falling into error; it is the function of the citizen to keep the Government from falling into error.”
—Robert H. [Houghwout] Jackson (1892–1954)