DLMF:1.14.E3 (Q495): 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.m1abdec
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.m2aadec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: Cauchy principal value / rank
 
Normal rank
Property / Symbols used: Cauchy principal value / qualifier
 
test:

⨍ a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}

\pvint_{\NVar{a}}^{\NVar{b}}
Property / Symbols used: Cauchy principal value / qualifier
 
xml-id: C1.S4.E24.m2adec
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.m1adec

Latest revision as of 15:21, 1 January 2020

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DLMF:1.14.E3
No description defined

    Statements

    test
    1 2 ⁢ ( f ⁢ ( u + ) + f ⁢ ( u - ) ) = 1 2 ⁢ π ⁢ ⨍ - ∞ ∞ F ⁢ ( x ) ⁢ e - i ⁢ x ⁢ u ⁢ d x , 1 2 𝑓 limit-from 𝑢 𝑓 limit-from 𝑢 1 2 𝜋 subscript superscript principal-value-integral 𝐹 𝑥 superscript 𝑒 𝑖 𝑥 𝑢 𝑥 {\displaystyle{\displaystyle\tfrac{1}{2}(f(u+)+f(u-))=\frac{1}{\sqrt{2\pi}}% \pvint^{\infty}_{-\infty}F(x)e^{-ixu}\mathrm{d}x,}}
    0 references
    DLMF id
    DLMF:1.14.E3
    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.m2abdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Cauchy principal value
    test
    ⨍ a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}
    xml-id
    C1.S4.E24.m2adec
    0 references
    Q10886
    test
    F ⁢ ( x ) 𝐹 𝑥 {\displaystyle{\displaystyle F(x)}}
    xml-id
    C1.S14.XMD1.m1adec
    0 references
     
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