Limit at Infinity of Sine Integral Function/Corollary
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Corollary to Limit at Infinity of Sine Integral Function
- $\ds \lim_{x \mathop \to -\infty} \map \Si x = -\frac \pi 2$
where $\Si$ denotes the sine integral function.
Proof
| \(\ds \map \Si {-x}\) | \(=\) | \(\ds -\map \Si x\) | Sine Integral Function is Odd | |||||||||||
| \(\ds \lim_{x \mathop \to -\infty} \map \Si x\) | \(=\) | \(\ds -\lim_{x \mathop \to +\infty} \map \Si x\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\frac \pi 2\) | Limit at Infinity of Sine Integral Function |
$\blacksquare$