EXPANSIONS OF CERTAIN INVERSE FACTORIAL SERIES VIA SERIES AND SEQUENCE TRANSFORMATIONS
Applicable Analysis and Discrete Mathematics, vol.20, no.1, pp.24-44, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 20 Issue: 1
- Publication Date: 2026
- Doi Number: 10.2298/aadm250816008d
- Journal Name: Applicable Analysis and Discrete Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO)
- Page Numbers: pp.24-44
- Keywords: Binomial transform, Euler sums, Harmonic numbers, Skew-harmonic numbers, Stirling numbers
- Akdeniz University Affiliated: Yes
Abstract
In this study, factorial series involving generalizations of the harmonic numbers are investigated. New expressions for the Dirichlet series (also called Euler sums) associated with hyperharmonic and skew-harmonic numbers are obtained. In addition, the relationships between the inverse factorial series of a given sequence and the inverse factorial series of the binomial, Stirling and Lah transformations of that sequence are investigated. Furthermore, closedform formulas are derived for inverse factorial series whose coefficients are given by the p-Stirling numbers.