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