Finite $q$-multiple harmonic sums on $1-\cdots-1,A,1-\cdots-1$ indices
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910009074384896 |
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| author | Ishikawa, Hideaki Komatsu, Takao |
| author_facet | Ishikawa, Hideaki Komatsu, Takao |
| contents | In this paper, we give explicit expressions about $q$-harmonic sums on $1-\cdots-1,A,1-\cdots-1$ indices. When $A=1$, many previous authors have studied and showed the identities, expressions, and properties. There are many results for explicit expressions about $q$-multiple zeta values or $q$-harmonic sums on $A-\cdots-A$ indices. Though there is the way to treat $q$-multiple zeta values unless the indices are the same, it has been successful to get the explicit expression of $q$-harmonic sums on $1-\cdots-1,A,1-\cdots-1$ indices when $A=2$. In this paper, we shall consider more general results when $A\ge 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02480 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite $q$-multiple harmonic sums on $1-\cdots-1,A,1-\cdots-1$ indices Ishikawa, Hideaki Komatsu, Takao Number Theory Combinatorics Primary 11M32, Secondary 05A15, 05A19, 05A30, 11B37, 11B73 In this paper, we give explicit expressions about $q$-harmonic sums on $1-\cdots-1,A,1-\cdots-1$ indices. When $A=1$, many previous authors have studied and showed the identities, expressions, and properties. There are many results for explicit expressions about $q$-multiple zeta values or $q$-harmonic sums on $A-\cdots-A$ indices. Though there is the way to treat $q$-multiple zeta values unless the indices are the same, it has been successful to get the explicit expression of $q$-harmonic sums on $1-\cdots-1,A,1-\cdots-1$ indices when $A=2$. In this paper, we shall consider more general results when $A\ge 3$. |
| title | Finite $q$-multiple harmonic sums on $1-\cdots-1,A,1-\cdots-1$ indices |
| topic | Number Theory Combinatorics Primary 11M32, Secondary 05A15, 05A19, 05A30, 11B37, 11B73 |
| url | https://arxiv.org/abs/2602.02480 |