DLMF:1.14.E4 (Q496): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1acdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec
Property / Symbols used
 
Property / Symbols used: Q10886 / rank
 
Normal rank
Property / Symbols used: Q10886 / qualifier
 
test:

F ⁢ ( x ) 𝐹 𝑥 {\displaystyle{\displaystyle F(x)}}

F(x)
Property / Symbols used: Q10886 / qualifier
 
xml-id: C1.S14.XMD1.m1bdec

Latest revision as of 15:22, 1 January 2020

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DLMF:1.14.E4
No description defined

    Statements

    test
    f ⁢ ( t ) = 1 2 ⁢ π ⁢ ∫ - ∞ ∞ F ⁢ ( x ) ⁢ e - i ⁢ x ⁢ t ⁢ d x . 𝑓 𝑡 1 2 𝜋 subscript superscript 𝐹 𝑥 superscript 𝑒 𝑖 𝑥 𝑡 𝑥 {\displaystyle{\displaystyle f(t)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}% F(x)e^{-ixt}\mathrm{d}x.}}
    0 references
    DLMF id
    DLMF:1.14.E4
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q10886
    test
    F ⁢ ( x ) 𝐹 𝑥 {\displaystyle{\displaystyle F(x)}}
    xml-id
    C1.S14.XMD1.m1bdec
    0 references
     
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