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DLMF:10.67.E10 - MaRDI portal

DLMF:10.67.E10 (Q4552)

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DLMF:10.67.E10
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    Statements

    DLMF defining formula
    ber ⁡ x ⁢ bei ′ ⁡ x - ber ′ ⁡ x ⁢ bei ⁡ x ∼ e x ⁢ 2 2 ⁢ π ⁢ x ⁢ ( 1 2 + 1 8 ⁢ 1 x + 9 64 ⁢ 2 ⁢ 1 x 2 + 39 512 ⁢ 1 x 3 + 75 8192 ⁢ 2 ⁢ 1 x 4 + ⋯ ) , asymptotic-expansion Kelvin-ber 𝑥 diffop Kelvin-bei 1 𝑥 diffop Kelvin-ber 1 𝑥 Kelvin-bei 𝑥 superscript 𝑒 𝑥 2 2 𝜋 𝑥 1 2 1 8 1 𝑥 9 64 2 1 superscript 𝑥 2 39 512 1 superscript 𝑥 3 75 8192 2 1 superscript 𝑥 4 ⋯ {\displaystyle{\displaystyle\operatorname{ber}x\operatorname{bei}'x-% \operatorname{ber}'x\operatorname{bei}x\sim\frac{e^{x\sqrt{2}}}{2\pi x}\left(% \frac{1}{\sqrt{2}}+\frac{1}{8}\frac{1}{x}+\frac{9}{64\sqrt{2}}\frac{1}{x^{2}}+% \frac{39}{512}\frac{1}{x^{3}}+\frac{75}{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.m3acdec
    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.m2acdec
    0 references
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aidec
    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.m2aidec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1idec
    0 references

    Identifiers

     
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