Formula:3056

Digital Library of Mathematical Functions ID 7.5.E12

${\displaystyle{\displaystyle|\mathcal{F}\left(x\right)|^{2}=2+{\mathrm{f}^{2}}\left(-x\right)+{\mathrm{g}^{2}}\left(-x\right)-2\sqrt{2}\cos\left(\tfrac{1}{4}\pi+\tfrac{1}{2}\pi x^{2}\right)\mathrm{f}\left(-x\right)-2\sqrt{2}\cos\left(\tfrac{1}{4}\pi-\tfrac{1}{2}\pi x^{2}\right)\mathrm{g}\left(-x\right),}}$

Constraint(s)

${\displaystyle{\displaystyle x\leq 0}}$

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
• ${\displaystyle{\displaystyle\mathcal{F}\left(\NVar{z}\right)}}$: Fresnel integral
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle x}}$: real variable
 

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