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DLMF:10.67.E13 - MaRDI portal

DLMF:10.67.E13 (Q4555)

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DLMF:10.67.E13
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    Statements

    DLMF defining formula
    ker 2 ⁡ x + kei 2 ⁡ x ∼ π 2 ⁢ x ⁢ e - x ⁢ 2 ⁢ ( 1 - 1 4 ⁢ 2 ⁢ 1 x + 1 64 ⁢ 1 x 2 + 33 256 ⁢ 2 ⁢ 1 x 3 - 1797 8192 ⁢ 1 x 4 + ⋯ ) , asymptotic-expansion Kelvin-ker 2 𝑥 Kelvin-kei 2 𝑥 𝜋 2 𝑥 superscript 𝑒 𝑥 2 1 1 4 2 1 𝑥 1 64 1 superscript 𝑥 2 33 256 2 1 superscript 𝑥 3 1797 8192 1 superscript 𝑥 4 ⋯ {\displaystyle{\displaystyle{\operatorname{ker}^{2}}x+{\operatorname{kei}^{2}}% x\sim\frac{\pi}{2x}e^{-x\sqrt{2}}\left(1-\frac{1}{4\sqrt{2}}\frac{1}{x}+\frac{% 1}{64}\frac{1}{x^{2}}+\frac{33}{256\sqrt{2}}\frac{1}{x^{3}}-\frac{1797}{8192}% \frac{1}{x^{4}}+\cdots\right),}}
    0 references
    Symbols used
    Kelvin function
    DLMF defining formula
    kei ν ⁡ ( x ) Kelvin-kei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E2.m3afdec
    0 references
    Kelvin function
    DLMF defining formula
    ker ν ⁡ ( x ) Kelvin-ker 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E2.m2afdec
    0 references
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aldec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aldec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aldec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1ldec
    0 references

    Identifiers

     
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