APPLICATIONS OF DERIVATIVE AND DIFFERENCE OPERATORS ON SOME SEQUENCES

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DİL A., Muniroglu E.

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, vol.14, no.2, pp.406-430, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.2298/aadm190908030d
  • Journal Name: APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.406-430
  • Keywords: Harmonic numbers, hyperharmonic numbers, generalized harmonic numbers, binomial coefficients, Fibonacci numbers, SUMS, SERIES
  • Akdeniz University Affiliated: Yes

Abstract

In this study, depending on the upper and the lower indices of the hyperharmonic number h(n)((r)), nonlinear recurrence relations are obtained. It is shown that generalized harmonic numbers and hyperharmonic numbers can be obtained from derivatives of the binomial coefficients. Taking into account of difference and derivative operators, several identities of the harmonic and hyperharmonic numbers are given. Negative-ordered hyperharmonic numbers are defined and their alternative representations are given.