Abstract
In this paper, we introduce a new type of generalized alternating hyperharmonic number \(H_n^{(p,r,s_{1},s_{2})}\), and show that the Euler sums of the generalized alternating hyperharmonic numbers \(H_n^{(p,r,s_{1},s_{2})}\) can be expressed in terms of linear combinations of the classical (alternating) Euler sums.
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Li, R. Euler sums of generalized alternating hyperharmonic numbers II. Ramanujan J 62, 383–411 (2023). https://doi.org/10.1007/s11139-023-00761-x
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DOI: https://doi.org/10.1007/s11139-023-00761-x
Keywords
- Generalized alternating hyperharmonic numbers
- Alternating Euler sums
- Truncated Faulhaber’s formula
- Combinatorial approach