DLMF:1.14.E28 (Q520)

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DLMF:1.14.E28
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    Statements

    Defining formula
    ℒ ⁡ ( f ′ ) ⁡ ( s ) = s ⁢ ℒ ⁡ ( f ) ⁡ ( s ) - f ⁢ ( 0 + ) - ∑ k = 1 n e - s ⁢ t k ⁢ ( f ⁢ ( t k + ) - f ⁢ ( t k - ) ) . Laplace-transform superscript 𝑓 ′ 𝑠 𝑠 Laplace-transform 𝑓 𝑠 𝑓 limit-from 0 subscript superscript 𝑛 𝑘 1 superscript 𝑒 𝑠 subscript 𝑡 𝑘 𝑓 limit-from subscript 𝑡 𝑘 𝑓 limit-from subscript 𝑡 𝑘 {\displaystyle{\displaystyle\mathscr{L}\left(f^{\prime}\right)\left(s\right)=s% \mathscr{L}\left(f\right)\left(s\right)-f(0+)-\sum^{n}_{k=1}e^{-st_{k}}(f(t_{k% }+)-f(t_{k}-)).}}
    0 references
    DLMF id
    DLMF:1.14.E28
    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.m2ajdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
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    Q10756
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1dec
    0 references
     
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