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DLMF:10.68.E17 - MaRDI portal

DLMF:10.68.E17 (Q4584)

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DLMF:10.68.E17
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    Statements

    DLMF defining formula
    ln ⁡ M ν ⁡ ( x ) = x 2 - 1 2 ⁢ ln ⁡ ( 2 ⁢ π ⁢ x ) - μ - 1 8 ⁢ 2 ⁢ 1 x - ( μ - 1 ) ⁢ ( μ - 25 ) 384 ⁢ 2 ⁢ 1 x 3 - ( μ - 1 ) ⁢ ( μ - 13 ) 128 ⁢ 1 x 4 + O ⁡ ( 1 x 5 ) , modulus-Bessel-M 𝜈 𝑥 𝑥 2 1 2 2 𝜋 𝑥 𝜇 1 8 2 1 𝑥 𝜇 1 𝜇 25 384 2 1 superscript 𝑥 3 𝜇 1 𝜇 13 128 1 superscript 𝑥 4 Big-O 1 superscript 𝑥 5 {\displaystyle{\displaystyle\ln M_{\nu}\left(x\right)=\frac{x}{\sqrt{2}}-\frac% {1}{2}\ln\left(2\pi x\right)-\frac{\mu-1}{8\sqrt{2}}\frac{1}{x}-\frac{(\mu-1)(% \mu-25)}{384\sqrt{2}}\frac{1}{x^{3}}-\frac{(\mu-1)(\mu-13)}{128}\frac{1}{x^{4}% }+O\left(\frac{1}{x^{5}}\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.m2aadec
    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
    modulus of Bessel functions
    DLMF defining formula
    M ν ⁡ ( x ) modulus-Bessel-M 𝜈 𝑥 {\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E1.m2aldec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1ndec
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    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1mdec
    0 references

    Identifiers

     
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