Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae–Stirling numbers

• Main Authors: Taekyun Kim, Dae San Kim, Lee-Chae Jang, Hyunseok Lee
• Format: Article
• Language: English
• Published: SpringerOpen 2020-05-01
• Series: Advances in Difference Equations
• Subjects: Jindalrae numbers and polynomials; Gaenari numbers and polynomials; Degenerate Stirling numbers of the first kind; Degenerate Stirling numbers of the second kind
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02701-1

Abstract The aim of this paper is to study Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae–Stirling numbers of the first and second kinds. For this purpose, we first introduce Jindalrae–Stirling numbers of the first and second kinds as extensions of the notions of the degenerate Stirling numbers of the first and second kinds, and deduce several relations involving those special numbers. Then we introduce Jindalrae and Gaenari numbers and polynomials and obtain some explicit expressions and identities associated with those numbers and polynomials. In addition, we interpret our results by using umbral calculus.