Method for obtaining coefficients of powers of bivariate generating functions

Статья в журнале

In this paper, we study methods for obtaining explicit formulas for the coefficients of generating functions. To solve this problem, we consider the methods that are based on using the powers of generating functions. We propose to generalize the concept of compositae to the case of generating functions in two variables and define basic operations on such compositae: composition, addition, multiplication, reciprocation and compositional inversion. These operations allow obtaining explicit formulas for compositae and coefficients of bivariate generating functions. In addition, we present several examples of applying the obtained results for getting explicit formulas for the coefficients of bivariate generating functions. The introduced mathematical apparatus can be used for solving different problems that are related to the theory of generating functions.

Журнал:

• Mathematics
• Multidisciplinary Digital Publishing Institute (Basel)
• Индексируется в Web of Science, Scopus

Библиографическая запись: Kruchinin, D. V. Method for obtaining coefficients of powers of bivariate generating functions [Electronic resource] / D. V. Kruchinin, V. V. Kruchinin, Y. V. Shablya // Mathematics. – 2021. – Vol. 9. – Iss. 4. – P. 428. - DOI: 10.3390/math9040428

Индексируется в:

• Scopus ( https://www.scopus.com/record/display.uri?eid=2-s2.0-85101877380&origin=resultslist )
• Web of science ( https://www.webofscience.com/wos/woscc/full-record/WOS:000624140600001 )
• РИНЦ ( https://www.elibrary.ru/item.asp?id=46761520 )