DLMF:9.13.E6 (Q2968): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11414 / rank
 
Normal rank
Property / Symbols used: Q11414 / qualifier
 
Defining formula:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q11414 / qualifier
 
xml-id: C9.S13.XMD3.m1ddec

Revision as of 14:58, 2 January 2020

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DLMF:9.13.E6
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    Statements

    Defining formula
    A n ⁡ ( - z ) = { p ⁢ z 1 / 2 ⁢ ( J - p ⁡ ( ζ ) + J p ⁡ ( ζ ) ) , n ⁢  odd , p 1 / 2 ⁢ B n ⁡ ( z ) , n ⁢  even , ODE-generalized-Airy-A 𝑛 𝑧 cases 𝑝 superscript 𝑧 1 2 Bessel-J 𝑝 𝜁 Bessel-J 𝑝 𝜁 𝑛  odd superscript 𝑝 1 2 ODE-generalized-Airy-B 𝑛 𝑧 𝑛  even {\displaystyle{\displaystyle A_{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}B_{n}\left(z\right),&n\text{ even},\end{cases}}}
    0 references
    DLMF id
    DLMF:9.13.E6
    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.m2adec
    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.m3abdec
    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.m4abdec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1ddec
    0 references
    parameter (locally)
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C9.S13.XMD1.m1ddec
    0 references
    Q11414
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C9.S13.XMD3.m1ddec
    0 references
     
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