An asymptotic expansion for an integral variant of the Wright operators - Abel, Ulrich; Patel, Prashantkumar G. (Modern Mathematical Methods, 2026)
In this work, we investigate an integral variant of the Wright operators arising in approximation theory. Our main contribution is the derivation of a complete pointwise asymptotic expansion for these operators \(W_n^{β, γ}\). To establish this expansion, we first develop several structural properties of the operators, emphasizing their intrinsic connections with special functions, including the Mittag-Leffler and confluent hypergeometric functions. The analysis requires a careful study of the moments of the associated integral operators and relies on a collection of auxiliary results, such as a localization theorem. The obtained asymptotic formula provides refined convergence estimates and yields deeper insight into the limiting behavior of the operators as \(n → ∞\).