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The list is missing entries (like, for derivatives) that are present on https://en.wikipedia.org/wiki/Laplace_transform -- this is confusing.
Also, my textbook (Modern Signals and Systems, Kwakernaak & Sivan, Prentice-Hall, 0-13-812728-X) also states one- and two-sided transforms
\delta^{(k)}(t) --> s^k [s\in C, k\in N]
and one-sided transform
1 --> 1/s [Re(s) > 0]
Being a mere user of the mathematics, I will not make these changes as I normally would.