DLMF:9.11.E4 (Q2911): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1bdec

Latest revision as of 14:48, 2 January 2020

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DLMF:9.11.E4
No description defined

    Statements

    test
    Ai 2 ⁡ ( z ) + Bi 2 ⁡ ( z ) = 1 π 3 / 2 ⁢ ∫ 0 ∞ exp ⁡ ( z ⁢ t - 1 12 ⁢ t 3 ) ⁢ t - 1 / 2 ⁢ d t . Airy-Ai 2 𝑧 Airy-Bi 2 𝑧 1 superscript 𝜋 3 2 superscript subscript 0 𝑧 𝑡 1 12 superscript 𝑡 3 superscript 𝑡 1 2 𝑡 {\displaystyle{\displaystyle{\mathrm{Ai}^{2}}\left(z\right)+{\mathrm{Bi}^{2}}% \left(z\right)=\frac{1}{\pi^{3/2}}\int_{0}^{\infty}\exp\left(zt-\tfrac{1}{12}t% ^{3}\right)t^{-1/2}\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:9.11.E4
    0 references
    Symbols used
    Q10919
    test
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1abdec
    0 references
    Q11081
    test
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1bdec
    0 references
     
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