DLMF:7.12.E3 (Q2414)

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DLMF:7.12.E3
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    Statements

    Defining formula
    g ⁡ ( z ) ∼ 1 π ⁢ z ⁢ ∑ m = 0 ∞ ( - 1 ) m ⁢ ( 1 2 ) 2 ⁢ m + 1 ( π ⁢ z 2 / 2 ) 2 ⁢ m + 1 , asymptotic-expansion Fresnel-auxilliary-function-g 𝑧 1 𝜋 𝑧 superscript subscript 𝑚 0 superscript 1 𝑚 Pochhammer 1 2 2 𝑚 1 superscript 𝜋 superscript 𝑧 2 2 2 𝑚 1 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)\sim\frac{1}{\pi z}\sum_{m% =0}^{\infty}(-1)^{m}\frac{{\left(\tfrac{1}{2}\right)_{2m+1}}}{(\pi z^{2}/2)^{2% m+1}},}}
    0 references
    DLMF id
    DLMF:7.12.E3
    0 references
    Symbols used
    auxiliary function for Fresnel integrals
    Defining formula
    g ⁡ ( z ) Fresnel-auxilliary-function-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E11.m2adec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q11312
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1bdec
    0 references
     
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