DLMF:10.21.E28 (Q3321): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: coefficients (locally) / rank
 
Normal rank
Property / Symbols used: coefficients (locally) / qualifier
 
Defining formula:

α ′ superscript 𝛼 ′ {\displaystyle{\displaystyle\alpha^{\prime}}}

\alpha^{\prime}
Property / Symbols used: coefficients (locally) / qualifier
 
xml-id: C10.S21.XMD6.m1adec

Latest revision as of 15:44, 2 January 2020

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DLMF:10.21.E28
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    Statements

    Defining formula
    𝒞 ν ⁡ ( σ ν ⁢ ( t ) ) ∼ ( 2 / ν ) 1 3 π ⁢ N ⁡ ( - 2 1 3 ⁢ α ′ ) ⁢ ∑ k = 0 ∞ β k ′ ν 2 ⁢ k / 3 , asymptotic-expansion cylinder-function 𝜈 subscript 𝜎 𝜈 𝑡 superscript 2 𝜈 1 3 𝜋 modulus-Airy-N superscript 2 1 3 superscript 𝛼 ′ superscript subscript 𝑘 0 subscript superscript 𝛽 ′ 𝑘 superscript 𝜈 2 𝑘 3 {\displaystyle{\displaystyle\mathscr{C}_{\nu}\left(\sigma_{\nu}(t)\right)\sim% \frac{(2/\nu)^{\frac{1}{3}}}{\pi N\left(-2^{\frac{1}{3}}\alpha^{\prime}\right)% }\sum_{k=0}^{\infty}\frac{\beta^{\prime}_{k}}{\nu^{2k/3}},}}
    0 references
    DLMF id
    DLMF:10.21.E28
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11afdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    Q11430
    Defining formula
    𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.Px5.p1.m3aedec
    0 references
    Airy modulus function
    Defining formula
    N ⁡ ( z ) modulus-Airy-N 𝑧 {\displaystyle{\displaystyle N\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E7.m2adec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1edec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1wdec
    0 references
    Q11461
    Defining formula
    σ ν ⁢ ( t ) subscript 𝜎 𝜈 𝑡 {\displaystyle{\displaystyle\sigma_{\nu}(t)}}
    xml-id
    C10.S21.XMD2.m1edec
    0 references
    Q11463
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C10.S21.XMD5.m1bdec
    0 references
    coefficients (locally)
    Defining formula
    α ′ superscript 𝛼 ′ {\displaystyle{\displaystyle\alpha^{\prime}}}
    xml-id
    C10.S21.XMD6.m1adec
    0 references
     
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