NEW SERIES WITH CAUCHY AND STIRLING NUMBERS, PART 2

Boyadzhiev K. N., KARGIN L.

Applicable Analysis and Discrete Mathematics, cilt.17, sa.1, ss.57-75, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.2298/aadm210112001b
  • Dergi Adı: Applicable Analysis and Discrete Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.57-75
  • Anahtar Kelimeler: Cauchy number, Harmonic number, Hyperharmonic number, Central binomial coefficient, Series with special numbers
  • Akdeniz Üniversitesi Adresli: Evet

Özet

We evaluate in closed form several series involving products of Cauchy numbers with other special numbers (harmonic, skew-harmonic, hyperharmonic, and central binomial). Similar results are obtained with series involving Stirling numbers of the first kind. We focus on several particular cases which give new closed forms for Euler sums of hyperharmonic numbers and products of hyperharmonic and harmonic numbers