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Pairs of functions with $\sum_{n} (f \circ g)(n) = \sum_{n} (g \circ f)(n) $
I was wondering there there are any pairs of functions $(f,g)$ such that $$\sum_{n=1}^{\infty} (f \circ g)(n) = \sum_{n=1}^{\infty} (g \circ f)(n) $$ on condition that they're not commutative with ...
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