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Extended Stirling numbers of the first kind associated with Daehee numbers and polynomials

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, we study the extended Stirling numbers of the first kind which have close connection with the r-Stirling numbers of the first kind and generalize the usual Stirling numbers of the first kind. We derive recurrence relations for those numbers and show their connections with the Stirling numbers of the first kind, higher-order Daehee polynomials and Bell polynomials. In addition, we introduce Daehee–Stirling numbers of the first kind and deduce their connections with the extended Stirling numbers of the first kind and r-Whitney numbers.

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Acknowledgements

The authors would like to thank the referee for his valuable suggestions and comments which improved the original manuscript greatly in its present form.

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Authors and Affiliations

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

    Taekyun Kim

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

    Dae San Kim

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  1. Taekyun Kim
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  2. Dae San Kim
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Correspondence to Taekyun Kim.

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Kim, T., Kim, D.S. Extended Stirling numbers of the first kind associated with Daehee numbers and polynomials. RACSAM 113, 1159–1171 (2019). https://doi.org/10.1007/s13398-018-0540-x

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  • DOI: https://doi.org/10.1007/s13398-018-0540-x

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