DLMF:2.3.E22 (Q741): Difference between revisions

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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.m1gdec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

P s ⁢ ( t ) subscript 𝑃 𝑠 𝑡 {\displaystyle{\displaystyle P_{s}(t)}}

P_{s}(t)
Property / Symbols used: function (locally) / qualifier
 
xml-id: C2.S3.XMD26.m1adec

Latest revision as of 16:54, 1 January 2020

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English
DLMF:2.3.E22
No description defined

    Statements

    Defining formula
    ∫ e i ⁢ x ⁢ p ⁢ ( t ) ⁢ P s ⁢ ( t ) ⁢ p ′ ⁢ ( t ) ⁢ d t , superscript 𝑒 𝑖 𝑥 𝑝 𝑡 subscript 𝑃 𝑠 𝑡 superscript 𝑝 ′ 𝑡 𝑡 {\displaystyle{\displaystyle\int e^{ixp(t)}P_{s}(t)p^{\prime}(t)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:2.3.E22
    0 references
    constraint
    s = 0 , 1 , 2 , … 𝑠 0 1 2 … {\displaystyle{\displaystyle s=0,1,2,\dots}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
    0 references
    Q10958
    Defining formula
    p ⁢ ( t ) 𝑝 𝑡 {\displaystyle{\displaystyle p(t)}}
    xml-id
    C2.S3.XMD17.m1gdec
    0 references
    function (locally)
    Defining formula
    P s ⁢ ( t ) subscript 𝑃 𝑠 𝑡 {\displaystyle{\displaystyle P_{s}(t)}}
    xml-id
    C2.S3.XMD26.m1adec
    0 references
     
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