User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/existence

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/integrand

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/evaluation

User:GFauxPas/Sandbox/Zeta2/FourierSeries/

User:GFauxPas/Sandbox/Zeta2/Informal Proof

$\mathcal L \left\{{}\right\}$

Theorem
Let $\mathcal L$ be the Laplace Transform.

Let $f, g$ be a functions such that $\mathcal L f$ and $\mathcal Lg$ exist.

Then $\mathcal L$ is a linear operator on $f$ and $g$:


 * $\forall \lambda \in \C: \mathcal L \left \{{\lambda f\left({t}\right) + g\left({t}\right)}\right\} = \lambda \mathcal L \{ {f\left({t}\right)}\} + \mathcal L \left\{ {g\left({t}\right)}\right\}$

everywhere all the above expressions are defined.