Extended Stirling numbers of the first kind associated with Daehee numbers and polynomials
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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.
KeywordsExtended Stirling numbers of the first kind Daehee numbers Daehee polynomials Daehee–Stirling numbers of the first kind
Mathematics Subject Classification11B73 11B83 05A19
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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