Formula:3048

Digital Library of Mathematical Functions ID 7.5.E4

${\displaystyle{\displaystyle S\left(z\right)=\tfrac{1}{2}-\mathrm{f}\left(z\right)\cos\left(\tfrac{1}{2}\pi z^{2}\right)-\mathrm{g}\left(z\right)\sin\left(\tfrac{1}{2}\pi z^{2}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}$: auxiliary function for Fresnel integrals
• ${\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}$: auxiliary function for Fresnel integrals
• ${\displaystyle{\displaystyle S\left(\NVar{z}\right)}}$: Fresnel integral
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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