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DLMF:9.12.E20 - MaRDI portal

DLMF:9.12.E20 (Q3646)

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DLMF:9.12.E20
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    Statements

    DLMF defining formula
    Hi ⁡ ( z ) = 1 π ⁢ ∫ 0 ∞ exp ⁡ ( - 1 3 ⁢ t 3 + z ⁢ t ) ⁢ d t , Scorer-Hi 𝑧 1 𝜋 superscript subscript 0 1 3 superscript 𝑡 3 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)=\frac{1}{\pi}\int_{0}^{% \infty}\exp\left(-\tfrac{1}{3}t^{3}+zt\right)\mathrm{d}t,}}
    0 references
    Symbols used
    Scorer function (inhomogeneous Airy function)
    DLMF defining formula
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2amdec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2amdec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    exponential function
    DLMF defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1pdec
    0 references

    Identifiers

     
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