DLMF:32.11.E19 (Q9454): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q12644 / rank
 
Normal rank
Property / Symbols used: Q12644 / qualifier
 
Defining formula:

ψ ( z ) 𝜓 𝑧 {\displaystyle{\displaystyle\psi(z)}}

\psi(z)
Property / Symbols used: Q12644 / qualifier
 
xml-id: C32.S11.XMD14.m1dec

Latest revision as of 14:15, 2 January 2020

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DLMF:32.11.E19
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    Statements

    w ( x ) = σ 1 2 x + σ ρ ( 2 x ) - 1 / 4 cos ( ψ ( x ) + θ ) + O ( x - 1 ) , 𝑤 𝑥 𝜎 1 2 𝑥 𝜎 𝜌 superscript 2 𝑥 1 4 𝜓 𝑥 𝜃 Big-O superscript 𝑥 1 {\displaystyle{\displaystyle w(x)=\sigma\sqrt{\tfrac{1}{2}x}+\sigma\rho(2x)^{-% 1/4}\cos\left(\psi(x)+\theta\right)+O\left(x^{-1}\right),}}
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    DLMF:32.11.E19
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    x + 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
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    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2aadec
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C32.S1.XMD3.m1mdec
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    σ 𝜎 {\displaystyle{\displaystyle\sigma}}
    C32.S11.XMD11.m1dec
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    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    C32.S11.XMD12.m1dec
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    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    C32.S11.XMD13.m1dec
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    ψ ( z ) 𝜓 𝑧 {\displaystyle{\displaystyle\psi(z)}}
    C32.S11.XMD14.m1dec
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