Applications of derivative and difference operators on some sequences
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...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | 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. |
|---|---|
| DOI: | 10.48550/arxiv.1910.01876 |