DLMF:2.5.E39 (Q815)

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DLMF:2.5.E39
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    Statements

    Defining formula
    I j ⁢ ( x ) = ∫ 0 ∞ e - t ⁢ h j ⁢ ( x ⁢ t ) ⁢ d t , subscript 𝐼 𝑗 𝑥 superscript subscript 0 superscript 𝑒 𝑡 subscript ℎ 𝑗 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle I_{j}(x)=\int_{0}^{\infty}e^{-t}h_{j}(xt)\mathrm{% d}t,}}
    0 references
    DLMF id
    DLMF:2.5.E39
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    constraint
    j = 1 , 2 𝑗 1 2 {\displaystyle{\displaystyle j=1,2}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
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    Q11005
    Defining formula
    h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}
    xml-id
    C2.S5.XMD16.m1kdec
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    Q11014
    Defining formula
    I j ⁢ ( x ) subscript 𝐼 𝑗 𝑥 {\displaystyle{\displaystyle I_{j}(x)}}
    xml-id
    C2.S5.XMD25.m1adec
    0 references
     
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