DLMF:9.5.E7 (Q2779): Difference between revisions

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

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2abdec

Revision as of 14:25, 2 January 2020

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DLMF:9.5.E7
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    Statements

    Defining formula
    Ai ⁡ ( z ) = e - ζ π ⁢ ∫ 0 ∞ exp ⁡ ( - z 1 / 2 ⁢ t 2 ) ⁢ cos ⁡ ( 1 3 ⁢ t 3 ) ⁢ d t , Airy-Ai 𝑧 superscript 𝑒 𝜁 𝜋 superscript subscript 0 superscript 𝑧 1 2 superscript 𝑡 2 1 3 superscript 𝑡 3 𝑡 {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{e^{-\zeta}}{\pi}% \int_{0}^{\infty}\exp\left(-z^{\ifrac{1}{2}}t^{2}\right)\cos\left(\tfrac{1}{3}% t^{3}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:9.5.E7
    0 references
    constraint
    | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\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.m1addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
     
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