Analytic Solvability of the H¨ormander Problem and the Borel Transformation of Multiple Laurent Series

Leinartas, Evgeny K.

doi:10.17516/1997-1397-2022-15-2-184-193

Cited by 1 publication

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“…Another task related to the development of algorithms for solving a multidimesional difference equation with constant, polynomial, or rational function coefficients can be found in [17]. There are also several studies on the multivariate case of the relationship between the generating function of a solution to a linear Cauchy problem [18][19][20]. These papers are only a small part of the research related to multivariate generating functions and confirm the relevance of the development of methods for processing such generating functions.…”

Section: Introductionmentioning

confidence: 97%

Method for Obtaining Coefficients of Powers of Multivariate Generating Functions

Kruchinin

Shablya

2023

Mathematics

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There are several general concepts that allow obtaining explicit formulas for the coefficients of generating functions in one variable by using their powers. One such concept is the application of compositae of generating functions. In previous studies, we have introduced a generalization for the compositae of multivariate generating functions and have defined basic operations on the compositae of bivariate generating functions. The use of these operations helps to obtain explicit formulas for compositae and coefficients of generating functions in two variables. In this paper, we expand these operations on compositae to the case of generating functions in three variables. In addition, we describe a way of applying compositae to obtain coefficients of rational generating functions in several variables. To confirm the effectiveness of using the proposed method, we present detailed examples of its application in obtaining explicit formulas for the coefficients of a generating function related to the Aztec diamond and a generating function related to the permutations with cycles.

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