Applications of derivative and difference operators on some sequences
| Autor: | Erkan Muniroğlu, Ayhan Dil |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Recurrence relation Mathematics - Number Theory Applied Mathematics Hyperharmonic number Harmonic (mathematics) Nonlinear system 39A70 11B37 11B65 33B15 11B39 Derivative (finance) Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Harmonic number Number Theory (math.NT) Combinatorics (math.CO) Analysis Binomial coefficient Mathematics |
| DOI: | 10.48550/arxiv.1910.01876 |
| Popis: | 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. Comment: 24 pages |
| Databáze: | OpenAIRE |
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