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DLMF:10.67.E9 - MaRDI portal

DLMF:10.67.E9 (Q4551)

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DLMF:10.67.E9
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    Statements

    DLMF defining formula
    ber 2 ⁡ x + bei 2 ⁡ x ∼ e x ⁢ 2 2 ⁢ π ⁢ x ⁢ ( 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-ber 2 𝑥 Kelvin-bei 2 𝑥 superscript 𝑒 𝑥 2 2 𝜋 𝑥 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{ber}^{2}}x+{\operatorname{bei}^{2}}% x\sim\frac{e^{x\sqrt{2}}}{2\pi x}\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
    bei ν ⁡ ( x ) Kelvin-bei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m3abdec
    0 references
    Kelvin function
    DLMF defining formula
    ber ν ⁡ ( x ) Kelvin-ber 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m2abdec
    0 references
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11ahdec
    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.m2ahdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1hdec
    0 references

    Identifiers

     
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