Article ID: MTJPAM-D-20-00011

Title: About Solving Some Functional Equations related to the Lagrange Inversion Theorem


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-20-00011; Volume 3 / Issue 1 / Year 2021, Pages 62-69

Document Type: Research Paper

Author(s): Dmitry V. Kruchinin a , Maria Y. Perminova b

aTomsk State University of Control Systems and Radioelectronics, Tomsk, Russia

bTomsk State University of Control Systems and Radioelectronics, Tomsk, Russia

Received: 1 May 2020, Accepted: 9 October 2020, Available online: 7 January 2021.

Corresponding Author: Dmitry V. Kruchinin (Email address: kdv@fb.tusur.ru)

Full Text: PDF

Abstract

Using the notion of the composita and the Lagrange inversion theorem, we present techniques for solving the functional equations B(x)=H(xB(x)r) and A(F(x)) = xH(A(x)), where H(x), B(x) and F(x) are known generating functions and A(x) is unknown, and r is a rational number. The first equation is a generalization of the Lagrange inversion formula for a rational power r in terms of compositae. For the second equation, the recurrent solution in terms of the compositae is obtained. Also we give some examples of the obtained results.

Keywords: Composita, Generating function, Lagrange inversion theorem, Functional equation

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