DLMF:9.12.E22 (Q2950): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aedec

Revision as of 14:55, 2 January 2020

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DLMF:9.12.E22
No description defined

    Statements

    test
    Hi ⁡ ( - z ) = 4 ⁢ z 2 3 3 / 2 ⁢ π 2 ⁢ ∫ 0 ∞ K 1 / 3 ⁡ ( t ) ζ 2 + t 2 ⁢ d t , Scorer-Hi 𝑧 4 superscript 𝑧 2 superscript 3 3 2 superscript 𝜋 2 superscript subscript 0 modified-Bessel-second-kind 1 3 𝑡 superscript 𝜁 2 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle\mathrm{Hi}\left(-z\right)=\frac{4z^{2}}{3^{3/2}% \pi^{2}}\int_{0}^{\infty}\frac{K_{1/3}\left(t\right)}{\zeta^{2}+t^{2}}\mathrm{% d}t,}}
    0 references
    DLMF id
    DLMF:9.12.E22
    0 references
    constraint
    | ph ⁡ z | < 1 3 ⁢ π phase 𝑧 1 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{3}\pi}}
    0 references
    Symbols used
    Scorer function (inhomogeneous Airy function)
    test
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2andec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aodec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
     
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