APPLICATIONS OF DERIVATIVE AND DIFFERENCE OPERATORS ON SOME SEQUENCES

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DİL A., Muniroglu E.

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, cilt.14, sa.2, ss.406-430, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.2298/aadm190908030d
  • 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.406-430
  • Anahtar Kelimeler: Harmonic numbers, hyperharmonic numbers, generalized harmonic numbers, binomial coefficients, Fibonacci numbers, SUMS, SERIES
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.