DLMF:9.6.E25 (Q2805)

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DLMF:9.6.E25
No description defined

    Statements

    Defining formula
    Bi ⁡ ( z ) = 1 3 1 / 6 ⁢ Γ ⁡ ( 2 3 ) ⁢ e - ζ ⁢ F 1 1 ⁡ ( 1 6 ; 1 3 ; 2 ⁢ ζ ) + 3 5 / 6 2 2 / 3 ⁢ Γ ⁡ ( 1 3 ) ⁢ ζ 2 / 3 ⁢ e - ζ ⁢ F 1 1 ⁡ ( 5 6 ; 5 3 ; 2 ⁢ ζ ) , Airy-Bi 𝑧 1 superscript 3 1 6 Euler-Gamma 2 3 superscript 𝑒 𝜁 Kummer-confluent-hypergeometric-M-as-1F1 1 6 1 3 2 𝜁 superscript 3 5 6 superscript 2 2 3 Euler-Gamma 1 3 superscript 𝜁 2 3 superscript 𝑒 𝜁 Kummer-confluent-hypergeometric-M-as-1F1 5 6 5 3 2 𝜁 {\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)=\frac{1}{3^{1/6}\Gamma% \left(\tfrac{2}{3}\right)}e^{-\zeta}{{}_{1}F_{1}}\left(\tfrac{1}{6};\tfrac{1}{% 3};2\zeta\right)+\frac{3^{5/6}}{2^{2/3}\Gamma\left(\tfrac{1}{3}\right)}\zeta^{% 2/3}e^{-\zeta}{{}_{1}F_{1}}\left(\tfrac{5}{6};\tfrac{5}{3};2\zeta\right),}}
    0 references
    DLMF id
    DLMF:9.6.E25
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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.m2andec
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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.m2abdec
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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.m7adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2andec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1xdec
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    change of variable (locally)
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S6.XMD1.m1mdec
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