DLMF:36.2.E5 (Q9840): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aadec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aadec
Property / Symbols used
 
Property / Symbols used: Q12749 / rank
 
Normal rank
Property / Symbols used: Q12749 / qualifier
 
Defining formula:

Φ ( U ) ⁡ ( s , t ; 𝐱 ) umbilic-catastrophe 𝑠 𝑡 𝐱 {\displaystyle{\displaystyle\Phi^{(\mathrm{U})}\left(\NVar{s},\NVar{t};\NVar{% \mathbf{x}}\right)}}

\umbcatastrophe@{\NVar{s}}{\NVar{t}}{\NVar{\mathbf{x}}}
Property / Symbols used: Q12749 / qualifier
 
xml-id: C36.S2.Px2.m2adec
Property / Symbols used
 
Property / Symbols used: Q12742 / rank
 
Normal rank
Property / Symbols used: Q12742 / qualifier
 
Defining formula:

t 𝑡 {\displaystyle{\displaystyle t}}

t
Property / Symbols used: Q12742 / qualifier
 
xml-id: C36.S1.XMD5.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12747 / rank
 
Normal rank
Property / Symbols used: Q12747 / qualifier
 
Defining formula:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q12747 / qualifier
 
xml-id: C36.S1.XMD6.m1bdec

Latest revision as of 15:03, 2 January 2020

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DLMF:36.2.E5
No description defined

    Statements

    Defining formula
    Ψ ( U ) ⁡ ( 𝐱 ) = ∫ - ∞ ∞ ∫ - ∞ ∞ exp ⁡ ( i ⁢ Φ ( U ) ⁡ ( s , t ; 𝐱 ) ) ⁢ d s ⁢ d t , umbilic-canonical-integral 𝐱 superscript subscript superscript subscript 𝑖 umbilic-catastrophe 𝑠 𝑡 𝐱 𝑠 𝑡 {\displaystyle{\displaystyle\Psi^{(\mathrm{U})}\left(\mathbf{x}\right)=\int_{-% \infty}^{\infty}\int_{-\infty}^{\infty}\exp\left(i\Phi^{(\mathrm{U})}\left(s,t% ;\mathbf{x}\right)\right)\mathrm{d}s\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:36.2.E5
    0 references
    constraint
    U = E , H U E H {\displaystyle{\displaystyle\mathrm{U}=\mathrm{E},\mathrm{H}}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q12749
    Defining formula
    Φ ( U ) ⁡ ( s , t ; 𝐱 ) umbilic-catastrophe 𝑠 𝑡 𝐱 {\displaystyle{\displaystyle\Phi^{(\mathrm{U})}\left(\NVar{s},\NVar{t};\NVar{% \mathbf{x}}\right)}}
    xml-id
    C36.S2.Px2.m2adec
    0 references
    Q12742
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C36.S1.XMD5.m1ddec
    0 references
    Q12747
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C36.S1.XMD6.m1bdec
    0 references
     
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