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