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DLMF:10.67.E11 - MaRDI portal

DLMF:10.67.E11 (Q4553)

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DLMF:10.67.E11
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    Statements

    DLMF defining formula
    ber ⁡ x ⁢ ber ′ ⁡ x + bei ⁡ x ⁢ bei ′ ⁡ x ∼ e x ⁢ 2 2 ⁢ π ⁢ x ⁢ ( 1 2 - 3 8 ⁢ 1 x - 15 64 ⁢ 2 ⁢ 1 x 2 - 45 512 ⁢ 1 x 3 + 315 8192 ⁢ 2 ⁢ 1 x 4 + ⋯ ) , asymptotic-expansion Kelvin-ber 𝑥 diffop Kelvin-ber 1 𝑥 Kelvin-bei 𝑥 diffop Kelvin-bei 1 𝑥 superscript 𝑒 𝑥 2 2 𝜋 𝑥 1 2 3 8 1 𝑥 15 64 2 1 superscript 𝑥 2 45 512 1 superscript 𝑥 3 315 8192 2 1 superscript 𝑥 4 ⋯ {\displaystyle{\displaystyle\operatorname{ber}x\operatorname{ber}'x+% \operatorname{bei}x\operatorname{bei}'x\sim\frac{e^{x\sqrt{2}}}{2\pi x}\left(% \frac{1}{\sqrt{2}}-\frac{3}{8}\frac{1}{x}-\frac{15}{64\sqrt{2}}\frac{1}{x^{2}}% -\frac{45}{512}\frac{1}{x^{3}}+\frac{315}{8192\sqrt{2}}\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.m3addec
    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.m2addec
    0 references
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11ajdec
    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.m2ajdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1jdec
    0 references

    Identifiers

     
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