DLMF:2.4.E14 (Q768)

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DLMF:2.4.E14
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    Statements

    Defining formula
    I ⁢ ( z ) = ∫ t 0 b e - z ⁢ p ⁢ ( t ) ⁢ q ⁢ ( t ) ⁢ d t - ∫ t 0 a e - z ⁢ p ⁢ ( t ) ⁢ q ⁢ ( t ) ⁢ d t , 𝐼 𝑧 superscript subscript subscript 𝑡 0 𝑏 superscript 𝑒 𝑧 𝑝 𝑡 𝑞 𝑡 𝑡 superscript subscript subscript 𝑡 0 𝑎 superscript 𝑒 𝑧 𝑝 𝑡 𝑞 𝑡 𝑡 {\displaystyle{\displaystyle I(z)=\int_{t_{0}}^{b}e^{-zp(t)}q(t)\mathrm{d}t-% \int_{t_{0}}^{a}e^{-zp(t)}q(t)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:2.4.E14
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
    0 references
    Q10972
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C2.S4.XMD11.m1edec
    0 references
    Q10980
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C2.S4.XMD12.m1bdec
    0 references
    contour integral (locally)
    Defining formula
    I ⁢ ( z ) 𝐼 𝑧 {\displaystyle{\displaystyle I(z)}}
    xml-id
    C2.S4.XMD13.m1bdec
    0 references
    Q10981
    Defining formula
    p ⁢ ( t ) 𝑝 𝑡 {\displaystyle{\displaystyle p(t)}}
    xml-id
    C2.S4.XMD15.m1cdec
    0 references
    Q10973
    Defining formula
    q ⁢ ( t ) 𝑞 𝑡 {\displaystyle{\displaystyle q(t)}}
    xml-id
    C2.S4.XMD16.m1idec
    0 references
     
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