DLMF:9.13.E7 (Q2969)

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DLMF:9.13.E7
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    Statements

    Defining formula
    B n ⁡ ( - z ) = { ( p ⁢ z ) 1 / 2 ⁢ ( J - p ⁡ ( ζ ) - J p ⁡ ( ζ ) ) , n ⁢  odd , p - 1 / 2 ⁢ A n ⁡ ( z ) , n ⁢  even . ODE-generalized-Airy-B 𝑛 𝑧 cases superscript 𝑝 𝑧 1 2 Bessel-J 𝑝 𝜁 Bessel-J 𝑝 𝜁 𝑛  odd superscript 𝑝 1 2 ODE-generalized-Airy-A 𝑛 𝑧 𝑛  even {\displaystyle{\displaystyle B_{n}\left(-z\right)=\begin{cases}(pz)^{1/2}\left% (J_{-p}\left(\zeta\right)-J_{p}\left(\zeta\right)\right),&n\text{ odd},\\ p^{-1/2}A_{n}\left(z\right),&n\text{ even}.\end{cases}}}
    0 references
    DLMF id
    DLMF:9.13.E7
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2aadec
    0 references
    Q11416
    Defining formula
    A n ⁡ ( z ) ODE-generalized-Airy-A 𝑛 𝑧 {\displaystyle{\displaystyle A_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C9.S13.SS1.p2.m3acdec
    0 references
    Q11417
    Defining formula
    B n ⁡ ( z ) ODE-generalized-Airy-B 𝑛 𝑧 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C9.S13.SS1.p2.m4acdec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1edec
    0 references
    parameter (locally)
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C9.S13.XMD1.m1edec
    0 references
    Q11414
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C9.S13.XMD3.m1edec
    0 references
    Q11415
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S13.XMD4.m1ddec
    0 references
     
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