Spivey-Type Recurrence Relations for Degenerate Bell and Dowling Polynomials
T. Kim, Dae San Kim
Abstract
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
Topics & Concepts
Degenerate energy levelsType (biology)Recurrence relationPure mathematicsMathematicsAlgebra over a fieldMathematical physicsPhysicsCombinatoricsQuantum mechanicsBiologyEcologyAdvanced Mathematical IdentitiesAdvanced Combinatorial MathematicsMathematical functions and polynomials