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DLMF:9.12.E8 - MaRDI portal

DLMF:9.12.E8 (Q3634)

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DLMF:9.12.E8
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    Statements

    DLMF defining formula
    - Gi ⁡ ( z ) , Ai ⁡ ( z ) , Bi ⁡ ( z ) , Scorer-Gi 𝑧 Airy-Ai 𝑧 Airy-Bi 𝑧 {\displaystyle{\displaystyle-\mathrm{Gi}\left(z\right),\mathrm{Ai}\left(z% \right),\mathrm{Bi}\left(z\right),}}
    0 references
    constraint
    | ph ⁡ z | ≤ 1 3 ⁢ π phase 𝑧 1 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{3}\pi}}
    0 references
    Symbols used
    Q10893
    DLMF defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1abdec
    0 references
    Q11055
    DLMF defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2addec
    0 references
    Scorer function (inhomogeneous Airy function)
    DLMF defining formula
    Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E4.m2aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    phase
    DLMF defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1edec
    0 references

    Identifiers

     
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