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On identities involving generalized harmonic, hyperharmonic and special numbers with Riordan arrays
| Content Provider | Scilit |
|---|---|
| Author | Koparal, Sibel Ömür, Neşe Duran, Ömer |
| Copyright Year | 2021 |
| Abstract | In this paper, by means of the summation property to the Riordan array, we derive some identities involving generalized harmonic, hyperharmonic and special numbers. For example, for n ≥ 0, ∑ k = 0 n B k k ! H ( n . k , α ) = α H ( n + 1 , 1 , α ) - H ( n , 1 , α ) , \sum\limits_{k = 0}^n {{{{B_k}} \over {k!}}H\left( {n.k,\alpha } \right) = \alpha H\left( {n + 1,1,\alpha } \right) - H\left( {n,1,\alpha } \right)} , and for n > r ≥ 0, ∑ k = r n - 1 ( - 1 ) k s ( k , r ) r ! α k k ! H n - k ( α ) = ( - 1 ) r H ( n , r , α ) , \sum\limits_{k = r}^{n - 1} {{{\left( { - 1} \right)}^k}{{s\left( {k,r} \right)r!} \over {{\alpha ^k}k!}}{H_{n - k}}\left( \alpha \right) = {{\left( { - 1} \right)}^r}H\left( {n,r,\alpha } \right)} , where Bernoulli numbers Bn and Stirling numbers of the first kind s (n, r). |
| Related Links | https://www.degruyter.com/document/doi/10.1515/spma-2020-0111/pdf |
| Ending Page | 30 |
| Page Count | 9 |
| Starting Page | 22 |
| e-ISSN | 23007451 |
| DOI | 10.1515/spma-2020-0111 |
| Journal | Special Matrices |
| Issue Number | 1 |
| Volume Number | 9 |
| Language | English |
| Publisher | Walter de Gruyter GmbH |
| Publisher Date | 2021-01-01 |
| Access Restriction | Open |
| Subject Keyword | Special Matrices Logic the Generalized Harmonic Number Riordan Arrays Stirling Number Journal: Special Matrices, Vol- 9 |
| Content Type | Text |
| Resource Type | Article |
