DLMF:9.6.E26 (Q2806)

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DLMF:9.6.E26
No description defined

    Statements

    Defining formula
    Bi ′ ⁡ ( z ) = 3 1 / 6 Γ ⁡ ( 1 3 ) ⁢ e - ζ ⁢ F 1 1 ⁡ ( - 1 6 ; - 1 3 ; 2 ⁢ ζ ) + 3 7 / 6 2 7 / 3 ⁢ Γ ⁡ ( 2 3 ) ⁢ ζ 4 / 3 ⁢ e - ζ ⁢ F 1 1 ⁡ ( 7 6 ; 7 3 ; 2 ⁢ ζ ) . diffop Airy-Bi 1 𝑧 superscript 3 1 6 Euler-Gamma 1 3 superscript 𝑒 𝜁 Kummer-confluent-hypergeometric-M-as-1F1 1 6 1 3 2 𝜁 superscript 3 7 6 superscript 2 7 3 Euler-Gamma 2 3 superscript 𝜁 4 3 superscript 𝑒 𝜁 Kummer-confluent-hypergeometric-M-as-1F1 7 6 7 3 2 𝜁 {\displaystyle{\displaystyle\mathrm{Bi}'\left(z\right)=\frac{3^{1/6}}{\Gamma% \left(\tfrac{1}{3}\right)}e^{-\zeta}{{}_{1}F_{1}}\left(-\tfrac{1}{6};-\tfrac{1% }{3};2\zeta\right)+\frac{3^{7/6}}{2^{7/3}\Gamma\left(\tfrac{2}{3}\right)}\zeta% ^{4/3}e^{-\zeta}{{}_{1}F_{1}}\left(\tfrac{7}{6};\tfrac{7}{3};2\zeta\right).}}
    0 references
    DLMF id
    DLMF:9.6.E26
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    Symbols used
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2aodec
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    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
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    Q11384
    Defining formula
    F 1 1 ⁡ ( a ; b ; z ) Kummer-confluent-hypergeometric-M-as-1F1 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle{{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}% \right)}}
    xml-id
    C16.S2.m7aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aodec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1ydec
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    change of variable (locally)
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S6.XMD1.m1ndec
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