DLMF:7.12.E6 (Q2417)

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DLMF:7.12.E6
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    Statements

    Defining formula
    R n ( f ) ⁢ ( z ) = ( - 1 ) n π ⁢ 2 ⁢ ∫ 0 ∞ e - π ⁢ z 2 ⁢ t / 2 ⁢ t 2 ⁢ n - ( 1 / 2 ) t 2 + 1 ⁢ d t , superscript subscript 𝑅 𝑛 Fresnel-auxilliary-function-f 𝑧 superscript 1 𝑛 𝜋 2 superscript subscript 0 superscript 𝑒 𝜋 superscript 𝑧 2 𝑡 2 superscript 𝑡 2 𝑛 1 2 superscript 𝑡 2 1 𝑡 {\displaystyle{\displaystyle R_{n}^{(\mathrm{f})}(z)=\frac{(-1)^{n}}{\pi\sqrt{% 2}}\int_{0}^{\infty}\frac{e^{-\pi z^{2}t/2}t^{2n-(1/2)}}{t^{2}+1}\mathrm{d}t,}}
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    DLMF id
    DLMF:7.12.E6
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    Symbols used
    auxiliary function for Fresnel integrals
    Defining formula
    f ⁡ ( z ) Fresnel-auxilliary-function-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E10.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.m2aedec
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