New applications of the Egorychev method of coefficients of integral representation and calculation of combinatorial sums

TL;DR

This paper explores novel applications of the Egorychev method for integral representations and combinatorial sums, extending its use to algebra and holomorphic function theory in complex spaces.

Contribution

It introduces new applications of the Egorychev method developed since the 1970s, particularly in algebra and complex analysis.

Findings

Extended the Egorychev method to algebraic structures

Applied the method to holomorphic functions in C^n

Demonstrated effectiveness in computing combinatorial sums

Abstract

Here we present the new applications of the Egorychev method of coefficients of integral representations and computation of combinatorial sums developed by the author at the end of 1970's and its recent applications to the algebra and the theory of holomorphic functions in C^n and others.