analyticity

Analyticity refers to a property of certain mathematical functions where they are infinitely differentiable and can be expressed as a power series (like an infinite sum of terms) around a point. This means the function's behavior can be precisely described using its derivatives, and it can be locally represented by a convergent series. Analytic functions are smooth and predictable, making them fundamental in complex analysis and many areas of mathematics and physics. Essentially, analyticity ensures that the function's values are closely linked to its local behavior, allowing detailed understanding and manipulation.