Difference between revisions of "Fresnel S"
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[[Fresnel S is odd]] <br /> | [[Fresnel S is odd]] <br /> | ||
[[Taylor series for Fresnel S]]<br /> | [[Taylor series for Fresnel S]]<br /> | ||
| − | + | [[Fresnel S in terms of erf]]<br /> | |
| − | [[Fresnel S in terms of | ||
[[Limiting value of Fresnel S]]<br /> | [[Limiting value of Fresnel S]]<br /> | ||
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=See Also= | =See Also= | ||
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=Videos= | =Videos= | ||
| − | [https://www.youtube.com/watch?v=fFZ6BsH99-0 The Fresnel Integral S(x) - How to integrate sin(x^2)]<br /> | + | [https://www.youtube.com/watch?v=fFZ6BsH99-0 The Fresnel Integral S(x) - How to integrate sin(x^2) (12 February 2015)]<br /> |
| − | + | [https://www.youtube.com/watch?v=H3uOq7VujYA Math and Physics: The Fresnel Integrals (12 May 2016)] <br /> | |
{{:*-integral functions footer}} | {{:*-integral functions footer}} | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest revision as of 17:21, 5 October 2016
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.)
Graph of $S$.
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)
