EXPANSIONS OF CERTAIN INVERSE FACTORIAL SERIES VIA SERIES AND SEQUENCE TRANSFORMATIONS

DİL A., Budak B.

Applicable Analysis and Discrete Mathematics, cilt.20, sa.1, ss.24-44, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.2298/aadm250816008d
  • Dergi Adı: Applicable Analysis and Discrete Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO)
  • Sayfa Sayıları: ss.24-44
  • Anahtar Kelimeler: Binomial transform, Euler sums, Harmonic numbers, Skew-harmonic numbers, Stirling numbers
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.