(untitled) (Analysis in Theory and Applications, 2026)
We present a new type of universal series, termed δ-universal series, for which the sum of squared coefficients satisfies _k=0^∞ |a_k|^2 < δ for an arbitrarily small δ > 0. We establish a version of Seleznev’s theorem within this framework. To construct such δ-universal series, we develop a variation of Mergelyan’s theorem.