DLMF:9.12.E23 (Q2951): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Scorer function (inhomogeneous Airy function) / rank
 
Normal rank
Property / Symbols used: Scorer function (inhomogeneous Airy function) / qualifier
 
test:

Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}

\ScorerGi@{\NVar{z}}
Property / Symbols used: Scorer function (inhomogeneous Airy function) / qualifier
 
xml-id: C9.S12.E4.m2amdec

Revision as of 13:55, 2 January 2020

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DLMF:9.12.E23
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    Statements

    test
    Gi ⁡ ( x ) = 4 ⁢ x 2 3 3 / 2 ⁢ π 2 ⁢ ⨍ 0 ∞ K 1 / 3 ⁡ ( t ) ζ 2 - t 2 ⁢ d t , Scorer-Gi 𝑥 4 superscript 𝑥 2 superscript 3 3 2 superscript 𝜋 2 superscript subscript principal-value-integral 0 modified-Bessel-second-kind 1 3 𝑡 superscript 𝜁 2 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle\mathrm{Gi}\left(x\right)=\frac{4x^{2}}{3^{3/2}\pi% ^{2}}\pvint_{0}^{\infty}\frac{K_{1/3}\left(t\right)}{\zeta^{2}-t^{2}}\mathrm{d% }t,}}
    0 references
    DLMF id
    DLMF:9.12.E23
    0 references
    constraint
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
    0 references
    Symbols used
    Scorer function (inhomogeneous Airy function)
    test
    Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E4.m2amdec
    0 references
     
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