Combinatorial sums, series and integrals involving odd harmonic numbers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929199252504576 |
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| author | Adegoke, Kunle Frontczak, Robert Goy, Taras |
| author_facet | Adegoke, Kunle Frontczak, Robert Goy, Taras |
| contents | We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyadzhiev from 2012 and Chen from 2016. Based on these generating functions we evaluate several infinite series in closed form. In addition, we offer some combinatorial sum identities involving Catalan numbers, harmonic numbers and odd harmonic numbers. Finally, we analyze a special log-integral with Fibonacci numbers and odd harmonic numbers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_02470 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combinatorial sums, series and integrals involving odd harmonic numbers Adegoke, Kunle Frontczak, Robert Goy, Taras Combinatorics 33B15, 11B39 We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyadzhiev from 2012 and Chen from 2016. Based on these generating functions we evaluate several infinite series in closed form. In addition, we offer some combinatorial sum identities involving Catalan numbers, harmonic numbers and odd harmonic numbers. Finally, we analyze a special log-integral with Fibonacci numbers and odd harmonic numbers. |
| title | Combinatorial sums, series and integrals involving odd harmonic numbers |
| topic | Combinatorics 33B15, 11B39 |
| url | https://arxiv.org/abs/2401.02470 |