DLMF:36.8.E5 (Q9949)

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DLMF:36.8.E5
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    Statements

    Defining formula
    f n ⁢ ( ζ , ζ ¯ ) = c n ⁢ ( ζ ) ⁢ c n ⁢ ( ζ ¯ ) ⁢ Ai ⁡ ( ζ ) ⁢ Bi ⁡ ( ζ ¯ ) + c n ⁢ ( ζ ) ⁢ d n ⁢ ( ζ ¯ ) ⁢ Ai ⁡ ( ζ ) ⁢ Bi ′ ⁡ ( ζ ¯ ) + d n ⁢ ( ζ ) ⁢ c n ⁢ ( ζ ¯ ) ⁢ Ai ′ ⁡ ( ζ ) ⁢ Bi ⁡ ( ζ ¯ ) + d n ⁢ ( ζ ) ⁢ d n ⁢ ( ζ ¯ ) ⁢ Ai ′ ⁡ ( ζ ) ⁢ Bi ′ ⁡ ( ζ ¯ ) , subscript 𝑓 𝑛 𝜁 𝜁 subscript 𝑐 𝑛 𝜁 subscript 𝑐 𝑛 𝜁 Airy-Ai 𝜁 Airy-Bi 𝜁 subscript 𝑐 𝑛 𝜁 subscript 𝑑 𝑛 𝜁 Airy-Ai 𝜁 diffop Airy-Bi 1 𝜁 subscript 𝑑 𝑛 𝜁 subscript 𝑐 𝑛 𝜁 diffop Airy-Ai 1 𝜁 Airy-Bi 𝜁 subscript 𝑑 𝑛 𝜁 subscript 𝑑 𝑛 𝜁 diffop Airy-Ai 1 𝜁 diffop Airy-Bi 1 𝜁 {\displaystyle{\displaystyle f_{n}(\zeta,\overline{\zeta})=c_{n}(\zeta)c_{n}(% \overline{\zeta})\mathrm{Ai}\left(\zeta\right)\mathrm{Bi}\left(\overline{\zeta% }\right)+c_{n}(\zeta)d_{n}(\overline{\zeta})\mathrm{Ai}\left(\zeta\right)% \mathrm{Bi}'\left(\overline{\zeta}\right)+d_{n}(\zeta)c_{n}(\overline{\zeta})% \mathrm{Ai}'\left(\zeta\right)\mathrm{Bi}\left(\overline{\zeta}\right)+d_{n}(% \zeta)d_{n}(\overline{\zeta})\mathrm{Ai}'\left(\zeta\right)\mathrm{Bi}'\left(% \overline{\zeta}\right),}}
    0 references
    DLMF id
    DLMF:36.8.E5
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    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1aadec
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    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2adec
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    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2adec
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    Q12755
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C36.S1.XMD3.m1ddec
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