DLMF:36.9.E8 (Q9961): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2abdec

Revision as of 15:12, 2 January 2020

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DLMF:36.9.E8
No description defined

    Statements

    Defining formula
    | Ψ ( H ) ⁡ ( x , y , z ) | 2 = 8 ⁢ π 2 ⁢ ( 2 9 ) 1 / 3 ⁢ ∫ - ∞ ∞ ∫ - ∞ ∞ Ai ⁡ ( ( 4 3 ) 1 / 3 ⁢ ( x + z ⁢ v + 3 ⁢ u 2 ) ) ⁢ Ai ⁡ ( ( 4 3 ) 1 / 3 ⁢ ( y + z ⁢ u + 3 ⁢ v 2 ) ) ⁢ d u ⁢ d v . superscript hyperbolic-umbilic-canonical-integral 𝑥 𝑦 𝑧 2 8 superscript 𝜋 2 superscript 2 9 1 3 superscript subscript superscript subscript Airy-Ai superscript 4 3 1 3 𝑥 𝑧 𝑣 3 superscript 𝑢 2 Airy-Ai superscript 4 3 1 3 𝑦 𝑧 𝑢 3 superscript 𝑣 2 𝑢 𝑣 {\displaystyle{\displaystyle\left|\Psi^{(\mathrm{H})}\left(x,y,z\right)\right|% ^{2}=8\pi^{2}\left(\frac{2}{9}\right)^{1/3}\int_{-\infty}^{\infty}\int_{-% \infty}^{\infty}\mathrm{Ai}\left(\left(\frac{4}{3}\right)^{1/3}(x+zv+3u^{2})% \right)\mathrm{Ai}\left(\left(\frac{4}{3}\right)^{1/3}(y+zu+3v^{2})\right)% \mathrm{d}u\mathrm{d}v.}}
    0 references
    DLMF id
    DLMF:36.9.E8
    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.m1aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
     
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