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DLMF:7.6.E6 - MaRDI portal

DLMF:7.6.E6 (Q3063)

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DLMF:7.6.E6
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    Statements

    DLMF defining formula
    S ⁡ ( z ) = ∑ n = 0 ∞ ( - 1 ) n ⁢ ( 1 2 ⁢ π ) 2 ⁢ n + 1 ( 2 ⁢ n + 1 ) ! ⁢ ( 4 ⁢ n + 3 ) ⁢ z 4 ⁢ n + 3 , Fresnel-sine-integral 𝑧 superscript subscript 𝑛 0 superscript 1 𝑛 superscript 1 2 𝜋 2 𝑛 1 2 𝑛 1 4 𝑛 3 superscript 𝑧 4 𝑛 3 {\displaystyle{\displaystyle S\left(z\right)=\sum_{n=0}^{\infty}\frac{(-1)^{n}% (\frac{1}{2}\pi)^{2n+1}}{(2n+1)!(4n+3)}z^{4n+3},}}
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    Symbols used
    Fresnel integral
    DLMF 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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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1edec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1edec
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    Identifiers

     
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