NEW SERIES WITH CAUCHY AND STIRLING NUMBERS, PART 2


Boyadzhiev K. N., KARGIN L.

Applicable Analysis and Discrete Mathematics, vol.17, no.1, pp.57-75, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.2298/aadm210112001b
  • Journal Name: Applicable Analysis and Discrete Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.57-75
  • Keywords: Cauchy number, Harmonic number, Hyperharmonic number, Central binomial coefficient, Series with special numbers
  • Akdeniz University Affiliated: Yes

Abstract

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