Some Properties of the $q$-Vietoris Number Sequence

Year 2025, Issue: 53, 36 - 46, 31.12.2025

Zehra Betül Gür , Serpil Halıcı

https://doi.org/10.53570/jnt.1778125

Abstract

This study aims to present the $q$-Vietoris numbers, a generalization of the Vietoris numbers, by using quantum calculus ($q$-calculus) and to investigate some of their algebraic properties, such as recurrence relations, a representation with the $q$-Gamma function, and some essential identities. Furthermore, it derives some finite summation formulas involving the $q$-harmonic numbers and the $q$-Vietoris numbers. Finally, the study discusses the need for further research.

Keywords

Vietoris numbers , central binomial coefficients , $q$-identities , harmonic numbers

Supporting Institution

Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Thanks

The first author is supported by the 2211-A Domestic Doctoral Fellowship by the Scientific and Technological Research Council of Türkiye (TÜBİTAK), Grant number: 1649B032102384.

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