  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 number and hyperharmonic number
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
number is defined and its alternative representations are given.
