C^{n+1
In mathematics, the notation C^n+1 refers to a class of functions that are continuously differentiable up to n+1 times. This means that not only the function itself is continuous, but also its first n+1 derivatives exist and are continuous. Such functions are important in calculus and analysis, as they exhibit smooth behavior.
The concept of C^n+1 is often used in the study of differential equations and in the field of smooth manifolds. Functions in this class are essential for ensuring that certain mathematical operations, like integration and differentiation, can be performed without encountering discontinuities or undefined behavior.