Spivey-Type Recurrence Relations for Degenerate Bell and Dowling Polynomials

Spivey showed a recurrence relation for the Bell numbers which are sums of the Stirling numbers of the second kind. Recently, the degenerate Bell polynomials and the degenerate Dowling polynomials were studied, whose coefficients are, respectively, the degenerate Stirling numbers of the second kind and the degenerate Whitney numbers of the second kind. The aim of this paper is to prove Spivey-type recurrence relations for those polynomials. In addition, a recurrence relation of the same type is shown for the degenerate r -Bell polynomials. DOI 10.1134/S1061920825020074