DLMF:36.2.E11 (Q9847): Difference between revisions

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

exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}

\exp@@{\NVar{z}}
Property / Symbols used: exponential function / qualifier
 
xml-id: C4.S2.E19.m2agdec

Revision as of 15:04, 2 January 2020

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DLMF:36.2.E11
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    Statements

    Defining formula
    Ψ ( U ) ⁡ ( 𝐱 ; k ) = k ⁢ ∫ - ∞ ∞ ∫ - ∞ ∞ exp ⁡ ( i ⁢ k ⁢ Φ ( U ) ⁡ ( s , t ; 𝐱 ) ) ⁢ d s ⁢ d t , diffraction-umbilic-catastrophe 𝐱 𝑘 𝑘 superscript subscript superscript subscript 𝑖 𝑘 umbilic-catastrophe 𝑠 𝑡 𝐱 𝑠 𝑡 {\displaystyle{\displaystyle\Psi^{(\mathrm{U})}(\mathbf{x};k)=k\int_{-\infty}^% {\infty}\int_{-\infty}^{\infty}\exp\left(ik\Phi^{(\mathrm{U})}\left(s,t;% \mathbf{x}\right)\right)\mathrm{d}s\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:36.2.E11
    0 references
    constraint
    k > 0 𝑘 0 {\displaystyle{\displaystyle k>0}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2agdec
    0 references
     
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