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Physics LibreTexts

14.6: A Function Times tⁿ

( \newcommand{\kernel}{\mathrm{null}\,}\)

I'll just give this one with out proof:

For n a positive integer,

L(tny)=(1)nd2ˉydsn.

Before proceeding further, I strongly recommend that you now apply theorems 14.3.1, 14.4.1, 14.5.1 and 14.6.1 to the several entries in your existing table of Laplace transforms and greatly expand your table of Laplace transforms. For example, you can already add (sinat)/t, teat and t2et to the list of functions for which you have calculated the Laplace transforms.


This page titled 14.6: A Function Times tⁿ is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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