Tomislav Buric

Appell Polynomials in Shifted Asymptotic Expansions: the Mills ratio, Hermite polynomials, and Stieltjes bounds

A theorem of Buri\'c, Elezovi\'c and Vuk\v si\'c states that translating the argument in an asymptotic expansion, $f(x)\sim\sum(-1)^na_nx^{-n-1}$, to $f(x+t)$, replaces the constant coefficients $a_n$ by the Appell polynomials $R_n(t)$ generated by $(a_n)$. Their motivating examples came from the gamma and polygamma fu...