Sine integral

The sine integral is defined by $$\mathrm{Si}(z) = \displaystyle\int_0^z \mathrm{sinc}(t) \mathrm{d}t, \quad |\mathrm{arg} \hspace{2pt} z|<\pi,$$ where $\mathrm{sinc}$ denotes the sinc function.

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  Graph of $\mathrm{Si}$.

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  Domain coloring of $\mathrm{Si}$.

Properties

Derivative of sine integral
Antiderivative of sine integral
Relationship between exponential integral Ei, cosine integral, and sine integral

Videos

Laplace Transform of Sine Integral (2 January 2015)

References

• 1956: Ian N. Sneddon: Special Functions of Mathematical Physics and Chemistry ... (previous) ... (next): $\S 5 (5.10)$
• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): $5.2.1$

$\ast$-integral functions

Cosine integral

Cosh integral

Exp integral $E_n$

Exp integral $\mathrm{Ei}$

Fresnel $C$

Fresnel $S$

Gudermannian

Inverse $\mathrm{gd}$

Sine integral

Log integral

Sinh integral