DLMF:7.5.E11 (Q2357)

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DLMF:7.5.E11
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    Statements

    Defining formula
    | ℱ ⁡ ( x ) | 2 = f 2 ⁡ ( x ) + g 2 ⁡ ( x ) , superscript Fresnel-integral 𝑥 2 Fresnel-auxilliary-function-f 2 𝑥 Fresnel-auxilliary-function-g 2 𝑥 {\displaystyle{\displaystyle|\mathcal{F}\left(x\right)|^{2}={\mathrm{f}^{2}}% \left(x\right)+{\mathrm{g}^{2}}\left(x\right),}}
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    DLMF id
    DLMF:7.5.E11
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    constraint
    x ≥ 0 𝑥 0 {\displaystyle{\displaystyle x\geq 0}}
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    Symbols used
    auxiliary function for Fresnel integrals
    Defining formula
    f ⁡ ( z ) Fresnel-auxilliary-function-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E10.m2aedec
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    auxiliary function for Fresnel integrals
    Defining formula
    g ⁡ ( z ) Fresnel-auxilliary-function-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E11.m2aedec
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    Fresnel integral
    Defining formula
    ℱ ⁡ ( z ) Fresnel-integral 𝑧 {\displaystyle{\displaystyle\mathcal{F}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E6.m2abdec
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    Q11313
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C7.S1.XMD1.m1dec
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