DLMF:9.12.E17 (Q2945)

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DLMF:9.12.E17
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    Statements

    Defining formula
    Hi ⁡ ( z ) = 3 - 2 / 3 π ⁢ ∑ k = 0 ∞ Γ ⁡ ( k + 1 3 ) ⁢ ( 3 1 / 3 ⁢ z ) k k ! , Scorer-Hi 𝑧 superscript 3 2 3 𝜋 superscript subscript 𝑘 0 Euler-Gamma 𝑘 1 3 superscript superscript 3 1 3 𝑧 𝑘 𝑘 {\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)=\frac{3^{-2/3}}{\pi}\sum% _{k=0}^{\infty}\Gamma\left(\frac{k+1}{3}\right)\frac{(3^{1/3}z)^{k}}{k!},}}
    0 references
    DLMF id
    DLMF:9.12.E17
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.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.m2akdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    Q11385
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1bdec
    0 references
     
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