DLMF:9.5.E6 (Q2778): 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.m1acdec

Revision as of 14:24, 2 January 2020

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DLMF:9.5.E6
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    Statements

    Defining formula
    Ai ⁡ ( z ) = 3 2 ⁢ π ⁢ ∫ 0 ∞ exp ⁡ ( - t 3 3 - z 3 3 ⁢ t 3 ) ⁢ d t , Airy-Ai 𝑧 3 2 𝜋 superscript subscript 0 superscript 𝑡 3 3 superscript 𝑧 3 3 superscript 𝑡 3 𝑡 {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{\sqrt{3}}{2\pi}% \int_{0}^{\infty}\exp\left(-\frac{t^{3}}{3}-\frac{z^{3}}{3t^{3}}\right)\mathrm% {d}t,}}
    0 references
    DLMF id
    DLMF:9.5.E6
    0 references
    constraint
    | ph ⁡ z | < 1 6 ⁢ π phase 𝑧 1 6 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{6}\pi}}
    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.m1acdec
    0 references
     
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