How do I prove L^(-1) {p^(bbbk)}=0 ?

Staffangz

Staffangz

Answered question

2022-09-11

Prove that L 1 { p k } = 0

Answer & Explanation

London Maldonado

London Maldonado

Beginner2022-09-12Added 13 answers

We know
L [ δ ( t ) ] = 1 L [ f ( t ) ] = s L [ f ( t ) ] ( s ) f ( 0 + )
So
L 1 [ s ] = L 1 [ L [ δ ( t ) ] δ ( 0 + ) ] = δ ( t )
Similarly,
L 1 ( s k ) = δ ( k ) ( t )
However we use Laplace transforms on functions which are only non-zero for t>0, which is why we would then take

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