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DLMF:10.21.E23 - MaRDI portal

DLMF:10.21.E23 (Q4004)

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DLMF:10.21.E23
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    Statements

    DLMF defining formula
    𝒞 ν ′ ⁡ ( ρ ν ⁢ ( t ) ) ∼ ( 2 / ν ) 2 3 π ⁢ M ⁡ ( - 2 1 3 ⁢ α ) ⁢ ∑ k = 0 ∞ β k ν 2 ⁢ k / 3 , asymptotic-expansion diffop cylinder-function 𝜈 1 subscript 𝜌 𝜈 𝑡 superscript 2 𝜈 2 3 𝜋 modulus-Airy-M superscript 2 1 3 𝛼 superscript subscript 𝑘 0 subscript 𝛽 𝑘 superscript 𝜈 2 𝑘 3 {\displaystyle{\displaystyle\mathscr{C}_{\nu}'\left(\rho_{\nu}(t)\right)\sim% \frac{(2/\nu)^{\frac{2}{3}}}{\pi M\left(-2^{\frac{1}{3}}\alpha\right)}\sum_{k=% 0}^{\infty}\frac{\beta_{k}}{\nu^{2k/3}},}}
    0 references
    Symbols used
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11addec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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    cylinder function
    DLMF 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.m3addec
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    Airy modulus function
    DLMF defining formula
    M ⁡ ( z ) modulus-Airy-M 𝑧 {\displaystyle{\displaystyle M\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E3.m2adec
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    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1cdec
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    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1udec
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    zero of cylinder function
    DLMF defining formula
    ρ ν ⁢ ( t ) subscript 𝜌 𝜈 𝑡 {\displaystyle{\displaystyle\rho_{\nu}(t)}}
    xml-id
    C10.S21.XMD1.m1gdec
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    coefficients (locally)
    DLMF defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C10.S21.XMD4.m1adec
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    coefficients
    DLMF defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C10.S21.XMD5.m1dec
    0 references

    Identifiers

     
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