DLMF:7.5.E2 (Q2348)

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DLMF:7.5.E2
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    Statements

    Defining formula
    C ⁡ ( z ) + i ⁢ S ⁡ ( z ) = 1 2 ⁢ ( 1 + i ) - ℱ ⁡ ( z ) . Fresnel-cosine-integral 𝑧 𝑖 Fresnel-sine-integral 𝑧 1 2 1 𝑖 Fresnel-integral 𝑧 {\displaystyle{\displaystyle C\left(z\right)+iS\left(z\right)=\tfrac{1}{2}(1+i% )-\mathcal{F}\left(z\right).}}
    0 references
    DLMF id
    DLMF:7.5.E2
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    Symbols used
    Fresnel integral
    Defining formula
    C ⁡ ( z ) Fresnel-cosine-integral 𝑧 {\displaystyle{\displaystyle C\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E7.m2adec
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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.m2adec
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    Fresnel integral
    Defining formula
    S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E8.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    Q11312
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1adec
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