DLMF:9.10.E4 (Q2886): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10919 / rank
 
Normal rank
Property / Symbols used: Q10919 / qualifier
 
Defining formula:

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

\AiryAi@{\NVar{z}}
Property / Symbols used: Q10919 / qualifier
 
xml-id: C9.S2.SS1.m1abdec

Revision as of 14:44, 2 January 2020

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DLMF:9.10.E4
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    Statements

    Defining formula
    ∫ x ∞ Ai ⁡ ( t ) ⁢ d t ∼ 1 2 ⁢ π - 1 / 2 ⁢ x - 3 / 4 ⁢ exp ⁡ ( - 2 3 ⁢ x 3 / 2 ) , asymptotically-equals superscript subscript 𝑥 Airy-Ai 𝑡 𝑡 1 2 superscript 𝜋 1 2 superscript 𝑥 3 4 2 3 superscript 𝑥 3 2 {\displaystyle{\displaystyle\int_{x}^{\infty}\mathrm{Ai}\left(t\right)\mathrm{% d}t\sim\tfrac{1}{2}\pi^{-1/2}x^{-3/4}\exp\left({-}\tfrac{2}{3}x^{3/2}\right),}}
    0 references
    DLMF id
    DLMF:9.10.E4
    0 references
    constraint
    x → ∞ → 𝑥 {\displaystyle{\displaystyle x\rightarrow\infty}}
    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.m1abdec
    0 references
     
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