DLMF:1.14.E29 (Q521): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Laplace transform / rank
 
Normal rank
Property / Symbols used: Laplace transform / qualifier
 
test:

( f ) ( s ) Laplace-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}

\Laplacetrans@{\NVar{f}}@{\NVar{s}}
Property / Symbols used: Laplace transform / qualifier
 
xml-id: C1.S14.E17.m2akdec

Revision as of 15:25, 1 January 2020

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DLMF:1.14.E29
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    ( f ( n ) ) ( s ) = s n ( 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+).}}
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    ( f ) ( s ) Laplace-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    C1.S14.E17.m2akdec
    0 references