English

Applications of derivative and difference operators on some sequences

Number Theory 2019-10-07 v1 Classical Analysis and ODEs Combinatorics

Abstract

In this study, depending on the upper and the lower indices of the hyperharmonic number hn(r)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.

Keywords

Cite

@article{arxiv.1910.01876,
  title  = {Applications of derivative and difference operators on some sequences},
  author = {Ayhan Dil and Erkan Muniroğlu},
  journal= {arXiv preprint arXiv:1910.01876},
  year   = {2019}
}

Comments

24 pages

R2 v1 2026-06-23T11:34:30.804Z