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DLMF:10.68.E19 - MaRDI portal

DLMF:10.68.E19 (Q4586)

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DLMF:10.68.E19
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    Statements

    DLMF defining formula
    N ν ⁡ ( x ) = e - x / 2 ⁢ ( π 2 ⁢ x ) 1 2 ⁢ ( 1 + μ - 1 8 ⁢ 2 ⁢ 1 x + ( μ - 1 ) 2 256 ⁢ 1 x 2 + ( μ - 1 ) ⁢ ( μ 2 + 14 ⁢ μ - 399 ) 6144 ⁢ 2 ⁢ 1 x 3 + O ⁡ ( 1 x 4 ) ) , modulus-Bessel-N 𝜈 𝑥 superscript 𝑒 𝑥 2 superscript 𝜋 2 𝑥 1 2 1 𝜇 1 8 2 1 𝑥 superscript 𝜇 1 2 256 1 superscript 𝑥 2 𝜇 1 superscript 𝜇 2 14 𝜇 399 6144 2 1 superscript 𝑥 3 Big-O 1 superscript 𝑥 4 {\displaystyle{\displaystyle N_{\nu}\left(x\right)=e^{-x/\sqrt{2}}\left(\frac{% \pi}{2x}\right)^{\frac{1}{2}}\left(1+\frac{\mu-1}{8\sqrt{2}}\frac{1}{x}+\frac{% (\mu-1)^{2}}{256}\frac{1}{x^{2}}+\frac{(\mu-1)(\mu^{2}+14\mu-399)}{6144\sqrt{2% }}\frac{1}{x^{3}}+O\left(\frac{1}{x^{4}}\right)\right),}}
    0 references
    Symbols used
    order not exceeding
    DLMF defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2acdec
    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.m2akdec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    modulus of derivatives of Bessel functions
    DLMF defining formula
    N ν ⁡ ( x ) modulus-Bessel-N 𝜈 𝑥 {\displaystyle{\displaystyle N_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E2.m2addec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1pdec
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    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1odec
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    Identifiers

     
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