Sunday, 18 August 2013

Shifted exponentials functions

Shifted exponentials functions

Define the set of functions $(f_m)$ for $m\in\mathbb{Z}$ where
$f:\mathbb{R}\to(0,\infty)$ is given by $$f_m(x)=\exp(x+m)$$ How is it
possible to prove that the functions $f_m$ are linearly independent over
$\mathbb{Q}$?

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