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

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.