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##f:\mathbb{R}\rightarrow \mathbb{R}_+ : f(x)=e^{-kx}##,

with ##k\in\mathbb{R}## is linearly independent. So is the set of sine functions

##f:\mathbb{R}\rightarrow [-1,1]: f(x) = \sin kx##,

with ##k\in\mathbb{R}_+##.

What about other kinds of special functions, would something like the set of gamma functions ##\Gamma (kx)## or sine integrals ##Si (kx)## also be linearly independent? Or the exponential integrals ##E_n (x)## of different integer orders ##n##?

Are there any good sources in literature that handle these questions?