DLMF:10.68.E20 (Q3890): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aadec

Revision as of 14:31, 2 January 2020

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DLMF:10.68.E20
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    Statements

    Defining formula
    ln ⁡ N ν ⁡ ( x ) = - x 2 + 1 2 ⁢ ln ⁡ ( π 2 ⁢ 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-N 𝜈 𝑥 𝑥 2 1 2 𝜋 2 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 N_{\nu}\left(x\right)=-\frac{x}{\sqrt{2}}+% \frac{1}{2}\ln\left(\frac{\pi}{2x}\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
    DLMF id
    DLMF:10.68.E20
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aldec
    0 references
    modulus of derivatives of Bessel functions
    Defining formula
    N ν ⁡ ( x ) modulus-Bessel-N 𝜈 𝑥 {\displaystyle{\displaystyle N_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E2.m2aedec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
     
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