Description : This work introduces the framework of Summatial Analysis, a mathematical approach to exact summation of structured series through the use of hypersummation operator and Bernoulli filtering techniques. The theory establishes a unified bridge between discrete summation processes and continuous integral representations. The hypersummation operator is used to transform classical series into analytically tractable forms, enabling exact evaluation of classes of infinite series that are typically handled through approximation methods. Bernoulli filtering plays a central role in eliminating polynomial contributions and isolating the effective summation structure. This paper develops some fundamental operator rules, and applies them to derive closed-form summation identities involving rational kernels and analytic functions. Summatial Analysis aims to provide a coherent structural framework for summation theory, connecting discrete mathematics, integral transforms, and complex analysis under a unified operational approach.
Pathy Kyungu (Mon,) studied this question.