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This note mainly concerns the binomial power function, defined as$(1+x^q)^{r}$. We construct systems of polynomials related to non-localapproximation, which allows us to establish the density results on $C[a,b]$,where $a,b\in\mathbb{R}$. As a corollary, we show that scattered translated ofpower functions and certain related functions are dense in the function spaces$L^p([a,b])$, for $1\leq p <\infty$.

On non-local approximation properties of the binomial power functions $(1+x^q)^r$