DLMF:7.6.E11 (Q2370)

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DLMF:7.6.E11
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    Statements

    Defining formula
    S ⁡ ( z ) = z ⁢ ∑ n = 0 ∞ 𝗃 2 ⁢ n + 1 ⁡ ( 1 2 ⁢ π ⁢ z 2 ) . Fresnel-sine-integral 𝑧 𝑧 superscript subscript 𝑛 0 spherical-Bessel-J 2 𝑛 1 1 2 𝜋 superscript 𝑧 2 {\displaystyle{\displaystyle S\left(z\right)=z\sum_{n=0}^{\infty}\mathsf{j}_{2% n+1}\left(\tfrac{1}{2}\pi z^{2}\right).}}
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    DLMF id
    DLMF:7.6.E11
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    Symbols used
    Fresnel integral
    Defining formula
    S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E8.m2abdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
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