Definition:Sine Integral Function

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The sine integral function is the real function $\Si: \R \to \R$ defined as:

$\map \Si x = \ds \int_{t \mathop \to 0}^{t \mathop = x} \frac {\sin t} t \rd t$



Also defined as

Some sources consider the value of the sine integral function at $x = 0$ as a special case:

$\map \Si x = \begin{cases} \ds \int_{t \mathop \to 0}^{t \mathop = x} \frac {\sin t} t \rd t & : x \ne 0 \\ \vphantom x \\ 0 & : x = 0 \\ \end{cases}$

but as $\map \Si 0 = 0$ as an emergent property of the sine integral function, this is not strictly necessary.

Also see

  • Results about the sine integral function can be found here.