DLMF:9.6.E13 (Q2793)

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DLMF:9.6.E13
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    Statements

    Defining formula
    I ± 1 / 3 ⁡ ( ζ ) = 1 2 ⁢ 3 / z ⁢ ( ∓ 3 ⁢ Ai ⁡ ( z ) + Bi ⁡ ( z ) ) , modified-Bessel-first-kind plus-or-minus 1 3 𝜁 1 2 3 𝑧 minus-or-plus 3 Airy-Ai 𝑧 Airy-Bi 𝑧 {\displaystyle{\displaystyle I_{\pm 1/3}\left(\zeta\right)=\tfrac{1}{2}\sqrt{3% /z}\left(\mp\sqrt{3}\mathrm{Ai}\left(z\right)+\mathrm{Bi}\left(z\right)\right)% ,}}
    0 references
    DLMF id
    DLMF:9.6.E13
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1afdec
    0 references
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2afdec
    0 references
    modified Bessel function of the first kind
    Defining formula
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2addec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1ldec
    0 references
    change of variable (locally)
    Defining formula
    ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    xml-id
    C9.S6.XMD2.m1cdec
    0 references
     
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