Fresnel S

The Fresnel $S$ function is defined by $$S(z)=\int_0^z \sin \left(t^2 \right) \mathrm{d}t.$$ (Note in Abramowitz&Stegun it is defined differently.)

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  Graph of $S$.

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  Domain coloring of Fresnel $S$.

Properties

Fresnel S is odd
Taylor series for Fresnel S
Fresnel S in terms of erf
Limiting value of Fresnel S

See Also

Fresnel C

Videos

The Fresnel Integral S(x) - How to integrate sin(x^2) (12 February 2015)
Math and Physics: The Fresnel Integrals (12 May 2016)

$\ast$-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