DLMF:10.67.E15 (Q3860): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1ndec

Latest revision as of 14:28, 2 January 2020

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DLMF:10.67.E15
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    Statements

    Defining formula
    ker ⁡ x ⁢ ker ′ ⁡ x + kei ⁡ x ⁢ kei ′ ⁡ x ∼ - π 2 ⁢ x ⁢ e - x ⁢ 2 ⁢ ( 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-ker 𝑥 diffop Kelvin-ker 1 𝑥 Kelvin-kei 𝑥 diffop Kelvin-kei 1 𝑥 𝜋 2 𝑥 superscript 𝑒 𝑥 2 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{ker}x\operatorname{ker}'x+% \operatorname{kei}x\operatorname{kei}'x\sim-\frac{\pi}{2x}e^{-x\sqrt{2}}\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
    DLMF id
    DLMF:10.67.E15
    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.m3ahdec
    0 references
    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.m2ahdec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11andec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2andec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2andec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1ndec
    0 references
     
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