Abstract
We consider a complete filtered Rota–Baxter (RB) algebra of weight [Formula: see text] over a commutative ring. Finding the unique solution of an inhomogeneous linear algebraic equation in this algebra, we generalize Spitzer’s identity in both commutative and non-commutative cases. As an application, considering the RB algebra of power series in one variable with q-integral as the RB operator, we show certain Eulerian identities.
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