DLMF:7.2.E10 (Q2332)

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DLMF:7.2.E10
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    Statements

    Defining formula
    f ⁡ ( z ) = ( 1 2 - S ⁡ ( z ) ) ⁢ cos ⁡ ( 1 2 ⁢ π ⁢ z 2 ) - ( 1 2 - C ⁡ ( z ) ) ⁢ sin ⁡ ( 1 2 ⁢ π ⁢ z 2 ) , Fresnel-auxilliary-function-f 𝑧 1 2 Fresnel-sine-integral 𝑧 1 2 𝜋 superscript 𝑧 2 1 2 Fresnel-cosine-integral 𝑧 1 2 𝜋 superscript 𝑧 2 {\displaystyle{\displaystyle\mathrm{f}\left(z\right)=\left(\tfrac{1}{2}-S\left% (z\right)\right)\cos\left(\tfrac{1}{2}\pi z^{2}\right)-\left(\tfrac{1}{2}-C% \left(z\right)\right)\sin\left(\tfrac{1}{2}\pi z^{2}\right),}}
    0 references
    DLMF id
    DLMF:7.2.E10
    0 references
    Symbols used
    Fresnel integral
    Defining formula
    C ⁡ ( z ) Fresnel-cosine-integral 𝑧 {\displaystyle{\displaystyle C\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E7.m2abdec
    0 references
    Fresnel integral
    Defining formula
    S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E8.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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