Symbols:C/Continuously Differentiable

Differentiability Class

$C^k$ or $\mathrm C^{\paren k}$

Let $f: \R \to \R$ be a real function.

Let $k \in \N$.

Then $\map f x$ is of differentiability class $C^k$ if and only if:

$\dfrac {\d^k} {\d x^k} \map f x \in C$

where $C$ denotes the class of continuous real functions.

That is, $f$ is in differentiability class $k$ if and only if there exists a $k$th derivative of $f$ which is continuous.

The $\LaTeX$ code for \(C^k\) is C^k .

The $\LaTeX$ code for \(\mathrm C^{\paren k}\) is \mathrm C^{\paren k} .

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): $\mathrm C^{\paren r}$