DLMF:7.5.E12 (Q2358)

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DLMF:7.5.E12
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    | ℱ ⁡ ( x ) | 2 = 2 + f 2 ⁡ ( - x ) + g 2 ⁡ ( - x ) - 2 ⁢ 2 ⁢ cos ⁡ ( 1 4 ⁢ π + 1 2 ⁢ π ⁢ x 2 ) ⁢ f ⁡ ( - x ) - 2 ⁢ 2 ⁢ cos ⁡ ( 1 4 ⁢ π - 1 2 ⁢ π ⁢ x 2 ) ⁢ g ⁡ ( - x ) , superscript Fresnel-integral 𝑥 2 2 Fresnel-auxilliary-function-f 2 𝑥 Fresnel-auxilliary-function-g 2 𝑥 2 2 1 4 𝜋 1 2 𝜋 superscript 𝑥 2 Fresnel-auxilliary-function-f 𝑥 2 2 1 4 𝜋 1 2 𝜋 superscript 𝑥 2 Fresnel-auxilliary-function-g 𝑥 {\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),}}
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    DLMF:7.5.E12
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