DLMF:1.14.E25 (Q517)

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DLMF:1.14.E25
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    Statements

    Defining formula
    ℒ ⁡ f ⁡ ( s ) = 1 1 - e - a ⁢ s ⁢ ∫ 0 a e - s ⁢ t ⁢ f ⁢ ( t ) ⁢ d t . Laplace-transform 𝑓 𝑠 1 1 superscript 𝑒 𝑎 𝑠 subscript superscript 𝑎 0 superscript 𝑒 𝑠 𝑡 𝑓 𝑡 𝑡 {\displaystyle{\displaystyle\mathscr{L}\mskip-3.0mu f\mskip 3.0mu \left(s% \right)=\frac{1}{1-e^{-as}}\int^{a}_{0}e^{-st}f(t)\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:1.14.E25
    0 references
    Symbols used
    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.m2agdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1asdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ardec
    0 references
     
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