Definition:Dirichlet Conditions

Definition
Let $\alpha, \beta \in \R$ be a real numbers such that $\alpha < \beta$.

Let $\map f x$ be a real function which is defined and bounded on the interval $\closedint \alpha \beta$.

The Dirichlet conditions on $f$ are sufficient conditions that $f$ must satisfy on $\closedint \alpha \beta$ in order for:
 * the Fourier series of $f$ at every $x$ in $\closedint \alpha \beta$ to equal $\map f x$
 * the behaviour of a Fourier series to be determined at finite discontinuities of $f$ in $\closedint \alpha \beta$:

They are as follows: