An analytic function is a function whose Taylor series converges for every x0 in its domain; as a corollary, analytic functions are infinitely differentiable. A case of special interest is a complex analytic function, which known as a holomorphic function.
Examples of analytic functions
- All polynomials
- Exponential and logarithmic functions
- Trigonometric functions
- Hyperbolic functions
- The gamma function (also holomorphic)
Examples of non-analytic functions
- Any discontinuous function, including absolute value and piecewise functions
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