Definition:Sine Integral Function
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Definition
The sine integral function is the real function $\Si: \R \to \R$ defined as:
- $\map \Si x = \begin{cases} \displaystyle \int_{t \mathop \to 0}^{t \mathop = x} \frac {\sin t} t \rd t & : x \ne 0 \\ \vphantom x \\ 0 & : x = 0 \\ \end{cases}$
Graph
Also see
- Results about the sine integral function can be found here.
Sources
- 1965: Murray R. Spiegel: Theory and Problems of Laplace Transforms ... (previous) ... (next): Chapter $1$: The Laplace Transform: Some Special Functions: $\text {V}$. The Sine and Cosine Integrals
- 2005: Roland E. Larson, Robert P. Hostetler and Bruce H. Edwards: Calculus (8th ed.): $\S 4$ P.S.
- Weisstein, Eric W. "Sine Integral." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SineIntegral.html