DLMF:7.12.E5 (Q3114)

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DLMF:7.12.E5
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    Statements

    DLMF defining formula
    g ⁡ ( z ) = 1 π ⁢ z ⁢ ∑ m = 0 n - 1 ( - 1 ) m ⁢ ( 1 2 ) 2 ⁢ m + 1 ( π ⁢ z 2 / 2 ) 2 ⁢ m + 1 , + R n ( g ) ⁢ ( z ) , Fresnel-auxilliary-function-g 𝑧 1 𝜋 𝑧 superscript subscript 𝑚 0 𝑛 1 superscript 1 𝑚 Pochhammer 1 2 2 𝑚 1 superscript 𝜋 superscript 𝑧 2 2 2 𝑚 1 superscript subscript 𝑅 𝑛 Fresnel-auxilliary-function-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)=\frac{1}{\pi z}\sum_{m=0}% ^{n-1}(-1)^{m}\frac{{\left(\tfrac{1}{2}\right)_{2m+1}}}{(\pi z^{2}/2)^{2m+1}},% +R_{n}^{(\mathrm{g})}(z),}}
    0 references
    Symbols used
    auxiliary function for Fresnel integrals
    DLMF defining formula
    g ⁡ ( z ) Fresnel-auxilliary-function-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E11.m2aadec
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    Q10733
    DLMF defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1addec
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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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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1ddec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1adec
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    Identifiers

     
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