DLMF:9.5.E4 (Q2776): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec

Revision as of 14:24, 2 January 2020

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DLMF:9.5.E4
No description defined

    Statements

    Defining formula
    Ai ⁡ ( z ) = 1 2 ⁢ π ⁢ i ⁢ ∫ ∞ ⁢ e - π ⁢ i / 3 ∞ ⁢ e π ⁢ i / 3 exp ⁡ ( 1 3 ⁢ t 3 - z ⁢ t ) ⁢ d t , Airy-Ai 𝑧 1 2 𝜋 𝑖 superscript subscript superscript 𝑒 𝜋 𝑖 3 superscript 𝑒 𝜋 𝑖 3 1 3 superscript 𝑡 3 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{1}{2\pi i}\int_{% \infty e^{-\pi i/3}}^{\infty e^{\pi i/3}}\exp\left(\tfrac{1}{3}t^{3}-zt\right)% \mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:9.5.E4
    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
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
     
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