Definition:Sine Integral Function

Definition
The sine integral function is the real function defined as:


 * $\operatorname{Si}: \R \to \R$:


 * $\operatorname{Si} \left({x}\right) = \begin{cases}

\displaystyle \int_{t \mathop \to 0}^{t \mathop = x} \frac {\sin t} t \, \mathrm d t & : x \ne 0 \\ \vphantom x \\ 0 & : x = 0 \\ \end{cases}$

Also see

 * Limit of Sine of $x$ over $x$
 * Dirichlet Integral