DLMF:1.14.E22 (Q514)

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DLMF:1.14.E22
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    Statements

    Defining formula
    ℒ ⁡ f a + ⁡ ( s ) = e - a ⁢ s ⁢ ℒ ⁡ f ⁡ ( s ) , Laplace-transform superscript subscript 𝑓 𝑎 𝑠 superscript 𝑒 𝑎 𝑠 Laplace-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{L}\mskip-3.0mu f_{a}^{+}\mskip 3.0mu % \left(s\right)=e^{-as}\mathscr{L}\mskip-3.0mu f\mskip 3.0mu \left(s\right),}}
    0 references
    DLMF id
    DLMF:1.14.E22
    0 references
    Symbols used
    Heaviside function
    Defining formula
    H ⁡ ( x ) Heaviside-H 𝑥 {\displaystyle{\displaystyle H\left(\NVar{x}\right)}}
    xml-id
    C1.S16.E13.m2adec
    0 references
    Laplace transform
    Defining formula
    ℒ ⁡ ( f ) ⁡ ( s ) Laplace-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    xml-id
    C1.S14.E17.m2addec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
     
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