Article ID: MTJPAM-D-24-00045

Title: Some identities for harmonic numbers based on composition of generating functions


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

Article ID: MTJPAM-D-24-00045; Volume 6 / Issue 3 / Year 2024, Pages 363-374

Document Type: Research Paper

Author(s): ‪Vladimir Kruchinin a , Dmitry Kruchinin b , Yuriy Shablya c

aTomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia

bTomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia – Sirius University of Science and Technology, 354340 Sochi, Russia

cTomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia

Received: 3 April 2024, Accepted: 10 December 2024, Published: 14 March 2025

Corresponding Author: Dmitry Kruchinin (Email address: KruchininDm@gmail.com)

Full Text: PDF

Abstract

In the paper we study the harmonic numbers and their properties. Applying a method of generating functions and a composition operation, we get a series of identities that are related to the harmonic, central binomial, triangular, Catalan and Mersenne numbers. We find a new generating function for the sum of products of the harmonic numbers and inverse binomial coefficients. Its integral representation is written. In addition, we provide examples of calculating infinite sums and obtaining identities.

Keywords: Generating function, harmonic numbers, central binomial numbers, Catalan numbers

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Cite this article

How to cite this article: V. Kruchinin, D. Kruchinin and Y. Shablya, Some identities for harmonic numbers based on composition of generating functions, Montes Taurus J. Pure Appl. Math. 6 (3), 363-374, 2024; Article ID: MTJPAM-D-24-00045.