A note on infinite series whose terms involve truncated degenerate exponentials. Issue 1 (31st December 2023)

• Record Type: Journal Article
• Authors: San Kim, Dae; Kim, Hyekyung; Kim, Taekyun
• Is Part Of: Applied mathematics in science and engineering. Volume 31:Issue 1(2023)
• Publication Date: 2023-12-31
• Subjects: Truncated degenerate exponentials -- degenerate Stirling numbers of the second kind -- generalized falling factorials; 11B83 -- 11B65 -- 11B73; Science -- Mathematics -- Periodicals; Engineering mathematics -- Periodicals; Applied mathematics -- Periodicals; 501.51
• DOI: 10.1080/27690911.2023.2205643
• Languages: English
• ISSNs: 2769-0911

Abstract

Abstract : The degenerate exponentials are degenerate versions of the ordinary exponential and the truncated degenerate exponentials are obtained from the Taylor expansions of them by truncating the first finitely many terms. The degenerate exponentials play an important role in recent studies on degenerate versions of many special numbers and polynomials, the degenerate gamma function, the degenerate umbral calculus and the degenerate q -umbral calculus. The aim of this note is to consider infinite series whose terms involve truncated degenerate exponentials together with binomial coefficients, the generalized falling factorials and the Stirling numbers of the second kind, and to find either their values or some other expressions of them as finite sums.