DLMF:2.3.E19 (Q738): 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.m1ajdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2ahdec
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.m2abdec
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.m3ajdec
Property / Symbols used
 
Property / Symbols used: Q10958 / rank
 
Normal rank
Property / Symbols used: Q10958 / qualifier
 
Defining formula:

p ⁢ ( t ) 𝑝 𝑡 {\displaystyle{\displaystyle p(t)}}

p(t)
Property / Symbols used: Q10958 / qualifier
 
xml-id: C2.S3.XMD17.m1edec
Property / Symbols used
 
Property / Symbols used: Q10961 / rank
 
Normal rank
Property / Symbols used: Q10961 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q10961 / qualifier
 
xml-id: C2.S3.XMD23.m1dec
Property / Symbols used
 
Property / Symbols used: Q10962 / rank
 
Normal rank
Property / Symbols used: Q10962 / qualifier
 
Defining formula:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q10962 / qualifier
 
xml-id: C2.S3.XMD24.m1dec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

q ⁢ ( t ) 𝑞 𝑡 {\displaystyle{\displaystyle q(t)}}

q(t)
Property / Symbols used: function (locally) / qualifier
 
xml-id: C2.S3.XMD6.m1edec

Latest revision as of 16:53, 1 January 2020

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English
DLMF:2.3.E19
No description defined

    Statements

    Defining formula
    I ⁢ ( x ) = ∫ a b e i ⁢ x ⁢ p ⁢ ( t ) ⁢ q ⁢ ( t ) ⁢ d t 𝐼 𝑥 superscript subscript 𝑎 𝑏 superscript 𝑒 𝑖 𝑥 𝑝 𝑡 𝑞 𝑡 𝑡 {\displaystyle{\displaystyle I(x)=\int_{a}^{b}e^{ixp(t)}q(t)\mathrm{d}t}}
    0 references
    DLMF id
    DLMF:2.3.E19
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
    0 references
    Q10958
    Defining formula
    p ⁢ ( t ) 𝑝 𝑡 {\displaystyle{\displaystyle p(t)}}
    xml-id
    C2.S3.XMD17.m1edec
    0 references
    Q10961
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C2.S3.XMD23.m1dec
    0 references
    Q10962
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C2.S3.XMD24.m1dec
    0 references
    function (locally)
    Defining formula
    q ⁢ ( t ) 𝑞 𝑡 {\displaystyle{\displaystyle q(t)}}
    xml-id
    C2.S3.XMD6.m1edec
    0 references
     
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