DLMF:10.61.E12 (Q3807)

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DLMF:10.61.E12
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    Statements

    Defining formula
    kei 1 2 ⁡ ( x ⁢ 2 ) = - ker - 1 2 ⁡ ( x ⁢ 2 ) = - 2 - 3 4 ⁢ π x ⁢ e - x ⁢ cos ⁡ ( x - π 8 ) . Kelvin-kei 1 2 𝑥 2 Kelvin-ker 1 2 𝑥 2 superscript 2 3 4 𝜋 𝑥 superscript 𝑒 𝑥 𝑥 𝜋 8 {\displaystyle{\displaystyle\operatorname{kei}_{\frac{1}{2}}\left(x\sqrt{2}% \right)=-\operatorname{ker}_{-\frac{1}{2}}\left(x\sqrt{2}\right)=-2^{-\frac{3}% {4}}\sqrt{\frac{\pi}{x}}e^{-x}\cos\left(x-\frac{\pi}{8}\right).}}
    0 references
    DLMF id
    DLMF:10.61.E12
    0 references
    Symbols used
    Kelvin function
    Defining formula
    kei ν ⁡ ( x ) Kelvin-kei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E2.m3agdec
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    Kelvin function
    Defining formula
    ker ν ⁡ ( x ) Kelvin-ker 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E2.m2agdec
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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.m2agdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2addec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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