DLMF:9.12.E7 (Q2935)

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DLMF:9.12.E7
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    Statements

    Defining formula
    Gi ′ ⁡ ( 0 ) = 1 2 ⁢ Hi ′ ⁡ ( 0 ) = 1 3 ⁢ Bi ′ ⁡ ( 0 ) = 1 / ( 3 5 / 6 ⁢ Γ ⁡ ( 1 3 ) ) = 0.14942 94524 ⁢ … . diffop Scorer-Gi 1 0 1 2 diffop Scorer-Hi 1 0 1 3 diffop Airy-Bi 1 0 1 superscript 3 5 6 Euler-Gamma 1 3 0.14942 94524 … {\displaystyle{\displaystyle\mathrm{Gi}'\left(0\right)=\tfrac{1}{2}\mathrm{Hi}% '\left(0\right)=\tfrac{1}{3}\mathrm{Bi}'\left(0\right)=1\Big{/}\left(3^{5/6}% \Gamma\left(\tfrac{1}{3}\right)\right)=0.14942\;94524\ldots.}}
    0 references
    DLMF id
    DLMF:9.12.E7
    0 references
    Symbols used
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2acdec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Scorer function (inhomogeneous Airy function)
    Defining formula
    Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E4.m2addec
    0 references
    Scorer function (inhomogeneous Airy function)
    Defining formula
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2addec
    0 references
     
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