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DLMF:1.14.E29 - MaRDI portal

DLMF:1.14.E29 (Q490)

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DLMF:1.14.E29
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    Statements

    DLMF defining formula
    ℒ ⁡ ( f ( n ) ) ⁡ ( s ) = s n ⁢ ℒ ⁡ ( f ) ⁡ ( s ) - s n - 1 ⁢ f ⁢ ( 0 + ) - s n - 2 ⁢ f ′ ⁢ ( 0 + ) - … - f ( n - 1 ) ⁢ ( 0 + ) . Laplace-transform superscript 𝑓 𝑛 𝑠 superscript 𝑠 𝑛 Laplace-transform 𝑓 𝑠 superscript 𝑠 𝑛 1 𝑓 limit-from 0 superscript 𝑠 𝑛 2 superscript 𝑓 ′ limit-from 0 … superscript 𝑓 𝑛 1 limit-from 0 {\displaystyle{\displaystyle\mathscr{L}\left(f^{(n)}\right)\left(s\right)=s^{n% }\mathscr{L}\left(f\right)\left(s\right)-s^{n-1}f(0+)-s^{n-2}f^{\prime}(0+)-% \dots-f^{(n-1)}(0+).}}
    0 references
    Symbols used
    Laplace transform
    DLMF 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.m2akdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1bdec
    0 references

    Identifiers

     
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