Some identities of degenerate harmonic and degenerate hyperharmonic numbers arising from umbral calculus-Reference-Cited by-同舟云学术

Some identities of degenerate harmonic and degenerate hyperharmonic numbers arising from umbral calculus

Published:2023-01-01 Issue:1 Volume:21 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Kim Taekyun¹,Kim Dae San²,Kim Hye Kyung³

Affiliation:

1. Department of Mathematics, Kwangwoon University , Seoul 139-701 , Republic of Korea

2. Department of Mathematics, Sogang University , Seoul 121-742 , Republic of Korea

3. Department of Mathematics Education, Daegu Catholic University , Gyeongsan 38430 , Republic of Korea

Abstract

Abstract Hyperharmonic numbers were introduced by Conway and Guy (The Book of Numbers, Copernicus, New York, 1996), whereas harmonic numbers have been studied since antiquity. Recently, the degenerate hyperharmonic and degenerate harmonic numbers were introduced as their respective degenerate versions. The aim of this article is to further investigate some properties and identities involving the degenerate hyperharmonic numbers and degenerate harmonic numbers. Especially, we derive some identities by making use of the transfer formula for associated sequences from umbral calculus.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2023-0124/pdf

Reference19 articles.

1. D. S. Kim and T. Kim, Degenerate Sheffer sequence and λ-Sheffer sequence, J. Math. Anal. Appl. 493 (2021), no. 1, 124521, DOI: https://doi.org/10.1016/j.jmaa.2020.124521.

2. T. Kim and D. S. Kim, Some identities on degenerate hyperharmonic numbers, Georgian Math. J. 30 (2022), no. 2, 255–262, DOI: https://doi.org/10.1515/gmj-2022-2203.

3. T. Kim and D. S. Kim, On some degenerate differential and degenerate difference operators, Russ. J. Math. Phys. 29 (2022), no. 1, 37–46, DOI: https://doi.org/10.1134/S1061920822010046.

4. T. Kim and D. S. Kim, Some identities on degenerate r-Stirling numbers via Boson operators, Russ. J. Math. Phys. 29 (2022), no. 4, 508–517, DOI: https://doi.org/10.1134/S1061920822040094.

5. T. Kim and D. S. Kim, Some identities involving degenerate Stirling numbers associated with several degenerate polynomials and numbers, Russ. J. Math. Phys. 30 (2023), no. 1, 62–75, DOI: https://doi.org/10.1134/S1061920823010041.

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