DLMF:9.11.E17 (Q2924): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11081 / rank
 
Normal rank
Property / Symbols used: Q11081 / qualifier
 
Defining formula:

Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}

\AiryBi@{\NVar{z}}
Property / Symbols used: Q11081 / qualifier
 
xml-id: C9.S2.SS1.m2aedec

Revision as of 14:50, 2 January 2020

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DLMF:9.11.E17
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    Statements

    Defining formula
    ∫ - ∞ ∞ Ai 2 ⁡ ( t ) ⁢ Bi ⁡ ( t ) ⁢ d t = Γ 2 ⁡ ( 1 3 ) 4 ⁢ 3 ⁢ π 2 . superscript subscript Airy-Ai 2 𝑡 Airy-Bi 𝑡 𝑡 Euler-Gamma 2 1 3 4 3 superscript 𝜋 2 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}{\mathrm{Ai}^{2}}\left(t% \right)\mathrm{Bi}\left(t\right)\mathrm{d}t=\frac{{\Gamma^{2}}\left(\frac{1}{3% }\right)}{4\sqrt{3}\pi^{2}}.}}
    0 references
    DLMF id
    DLMF:9.11.E17
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1ahdec
    0 references
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2aedec
    0 references
     
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